Research Article Analytic Approximate Solution for Falkner-Skan …downloads.hindawi.com/journals/tswj/2014/617453.pdf · 2019-07-31 · Research Article Analytic Approximate Solution

Research ArticleAnalytic Approximate Solution for Falkner-Skan Equation

Vasile Marinca12 Remus-Daniel Ene3 and Bogdan Marinca4

1 Department of Mechanics and Vibration Politehnica University of Timisoara 300222 Timisoara Romania2Department of Electromechanics and Vibration Center for Advanced and Fundamental Technical ResearchRomania Academy 300223 Timisoara Romania

3 Department of Mathematics Politehnica University of Timisoara 300006 Timisoara Romania4Department of Applied Electronics Politehnica University of Timisoara 300223 Timisoara Romania

Correspondence should be addressed to Remus-Daniel Ene eneremusgmailcom

Received 14 January 2014 Accepted 10 March 2014 Published 30 April 2014

Academic Editors M Han Z Jin and Y Xia

Copyright copy 2014 Vasile Marinca et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper deals with the Falkner-Skan nonlinear differential equation An analytic approximate technique namely optimalhomotopy asymptotic method (OHAM) is employed to propose a procedure to solve a boundary-layer problem Ourmethod doesnot depend upon small parameters and provides us with a convenient way to optimally control the convergence of the approximatesolutions The obtained results reveal that this procedure is very effective simple and accurate A very good agreement was foundbetween our approximate results and numerical solutions which prove that OHAM is very efficient in practice ensuring a veryrapid convergence after only one iteration

1 Introduction

It is known that the word ldquoviscoelasticrdquo means the simultane-ous existence of viscous and simultaneous elastic responsesof a material Some materials having a viscoelastic behaviorare relevant in many fields of study for industrial and tech-nological applications such as polymers plastic processingcosmetics geology composites paint flow adhesives towersgenerators accelerators electrostatic filters droplet filtersand the design of heat exchanges [1]

Motivated by significant applications of viscoelasticmate-rials a substantial amount of research works has beeninvested in the study of nonlinear systems In 1931 Falknerand Skan [2] have used some approximate procedures to solveboundary-layer equations Hartree [3] found the numericalsolution using a shootingmethodwith 11986510158401015840(0) (see (7)) as freeparameter The boundary conditions (8) arise in the study ofviscous flow past a wedge of angle 120573120587 120573 gt 0 correspondsto flow toward the wedge and 120573 lt 0 corresponds to flowaway from the wedge The special case 120573 = 0 is called theBlasius equation where the wedge reduced to a flat plate In[4 5] it is proved that if 0 le 120573 le 1 then the Falkner-Skan equation (7) with initial conditions (8) admits a unique

smooth solution For minus01988 lt 120573 lt 0 there exist twosolutions that is one with 11986510158401015840(0) gt 0 and the other onewith 11986510158401015840(0) lt 0 Botta et al [6] showed that the solutionof Falkner-Skan equation is unique for 120573 gt 1 under therestriction 0 lt 119865

1015840(0) lt 1 Forced convection boundary-

layer flow over a wedge with uniform suction or injectionis analyzed by Yih [7] Asaithambi [8] studied the Falkner-Skan equation using finite difference scheme In [9] Zaturskaand Banks presented a new solution branch in function ofparameter 120573 This solution branch is found to end singularityat 120573 = 1 its structure is analytically investigated andthe principal characteristics are described Also the spatialstability of such solutions is commented on The differentialtransformation is adopted to investigate the velocity andshear-stress fields associated with Falkner-Skan boundary-layer problem in [10] A group of transformations is used toreduce the boundary value problem into a pair of initial valueproblems which are then solved by means of the differentialtransformation method The nonlinear ordinary differentialequation is solved using Adomian decomposition method(ADM) by Elgazery [11] such that the condition at infinitywas applied to a related Pade approximation and Laplacetransformation to the obtained solution Also ADM is used in

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 617453 22 pageshttpdxdoiorg1011552014617453

2 The Scientific World Journal

[12] byAlizadeh et al to find an analytical solution in the formof infinite power series Magnetohydrodynamic effects onthe Falkner-Skan wedge flow are studied by Abbasbandy andHayat in [13]The same authors usedHankel-Pade and homo-topy analysis method for the derivation of the solutions [14]From a fluidmechanical point of view the pathophysiologicalsituation in myocardical bridges involves fluid flow in atime dependent flow geometry caused by contracting cardiacmuscles overlying an intramural segment of the coronaryartery A boundary-layer model for the calculation of thepressure drop and flow separation is presented in [15] underthe assumption that the idealized flow through a constrictionis given by near equilibrium velocity profiles of the Falkner-Skan-Cooke family the evolution of the boundary-layer isobtained by the simultaneous solution of the Falkner-Skanequation and the transient non-Karman integral momentumequation

Pirkhedri et al [16] developed a numerical techniquetransforming the governing partial differential equation intoa nonlinear third-order boundary value problemby similarityvariables and then solved it by the rational Legendre collo-cation method It used transformed Hermite-Gauss nodesas interpolation points The steady Falkner-Skan solution forgravity-driven film flow of micropolar fluid is investigated in[17] The ordinary differential equations are solved numeri-cally using an implicit finite difference scheme known as theKeller-box method In [18] Lakestani truncated the semi-infinite physical domain of the problem to a finite domainexpanding the required approximate solution as the elementsof Chebyshev cardinal functions Yun proposed in [19] aniterative method for solving the Falkner-Skan equation in theform of polynomial series without requiring any differenti-ations or integrations of the previous iterate solutions Theauthor suggests a correction method which is compared withthe successive differences of the iterations In [20] Hendi andHussain considered Falkner-Skan flow over a porous surfacetaking into account the case of uniform suctionblowingStream function formulation and suitable transformationsreduce the arising problem to ordinary differential equationwhich has been solved by homotopy analysis method

In science and engineering there exist a lot of nonlineardifferential equations and even strongly nonlinear problemswhich are still very difficult to solve analytically by using tra-ditional methods Many methods exist for approximating thesolutions of nonlinear problems for example the Adomiandecompositionmethod [21] themodifiedLindstedt-Poincaremethod [22] the parameter-expansion method [23] optimalvariational method [24] optimal homotopy perturbationmethod [25] and so on [26]

The aim of the present paper is to propose an accurateapproach to Falkner-Skan equation using an analytical tech-nique namely optimal homotopy asymptotic method [26ndash28]

The validity of our procedure which does not imply thepresence of a small parameter in the equation is based onthe construction and determination of the auxiliary functionscombined with a convenient way to optimally control theconvergence of the solution The efficiency of the proposedprocedure is proved while an accurate solution is explicitly

analytically obtained in an iterative way after only oneiteration

2 The Governing Equation

The two-dimensional laminar boundary-layer equations ofan incompressible fluid subject to a pressure gradient are[2 3 9 12]

119906120597119906

120597119909+ V

120597119906

120597119910= minus

1

1205881199011015840+ ]

1205972119906

1205971199102 (1)

120597119906

120597119909+120597V120597119910

= 0 (2)

where 1199011015840 is the pressure gradient 1199011015840 = minus120588119880(120597119880120597119909) 119906 isthe streamwise velocity in the direction of the fluid flow Vis the velocity in the direction normal to 119906 ] is the constantkinematic viscosity and119880(119909) is the velocity at the edge of theboundary-layer which obeys the power-law relation 119880(119909) =119886119909119898 (119909 gt 0) where 119886 is the mean stream velocity and 119898 is

a constant The relevant boundary conditions for fixed plateare

119910 = 0 119906 = 0 V = 0 119906 997888rarr 119886 as 119910 997888rarr infin (3)

A stream function 120595(119909 119910) is introduced such that

119906 =120597120595

120597119910 V = minus

120597120595

120597119909 (4)

Equation (2) of continuity is satisfied identically Themomentum equation (1) becomes

120597120595

120597119910

1205972120595

120597119909120597119910minus120597120595

120597119909

1205972120595

1205971199102= 119880

120597119880

120597119909+ ]

1205973120595

1205971199103 (5)

Integrating (5) and using similarity variable yield

120595 = 119909(1+119898)2

radic2]1198861 + 119898

119865 (120578)

120578 =119910

119909(1minus119898)2radic(1 + 119898) 119886

2]

(6)

Substituting (6) into (5) gives the equation of Falkner-Skan in the form

119865101584010158401015840(120578) + 119865 (120578) 119865

10158401015840(120578) + 120573 (1 minus 119865

1015840(120578)2

) = 0 (7)

with the initial and boundary conditions

119865 (0) = 0 1198651015840

(0) = 0 1198651015840

(infin) = 0 (8)

where 120573 = 2119898(119898 + 1) is a measure of the pressure gradientand prime denotes derivative with respect to 120578

The Scientific World Journal 3

3 Fundamentals of the OHAM

In what follows we consider nonlinear differential equation

119871 (119865 (120578)) + 119873 (119865 (120578)) = 0 (9)

with boundaryinitial condition

119861 (119865 1198651015840 11986510158401015840 ) = 0 (10)

In (9) 119871 is a linear operator and 119873 is a nonlinear opera-tor In (10) 119861 is a boundary operator

According to the basic ideas of OHAM [26ndash28] oneconstructs a family of equations

(1 minus 119901) 119871 (F (120578 119901))

= 119867 (120578 119901) [119871 (F (120578 119901)) + 119873 (F (120578 119901))]

(11)

The boundary condition is

119861(F (120578 119901) 120597F (120578 119901)

1205971205781205972F (120578 119901)

1205971205782 ) = 0 (12)

where 120578 isin R F(120578 119901) is an unknown function 119901 isin [0 1] isan embedding parameter and119867(120578 119901) is an auxiliary functionsuch that 119867(120578 0) = 0 and 119867(120578 119901) = 0 for 119901 = 0 When 119901increases from 0 to 1 the solution F(120578 119901) changes frominitial approximation 119865

0(120578) to the solution 119865(120578) For 119901 = 0

and 119901 = 1 it holds that respectively

F (120578 0) = 1198650(120578) F (120578 1) = 119865 (120578) (13)

Expanding F(120578 119901) in series with respect to the parame-ter 119901 one has

F (120578 119901) = 1198650(120578) + 119901119865

1(120578) + 119901

21198652(120578) + sdot sdot sdot (14)

The series (14) contains the auxiliary function 119867(120578 119901)which determines their convergence region For the auxiliaryfunction 119867(120578 119901) we propose that

119867(120578 119901) = 1199011198671(120578 119862119895) + 11990121198672(120578 119862119895) + sdot sdot sdot (15)

where 119867119894(120578 119862119895) and 119894 = 1 2 are functions of variable 120578

and of a number of unknown parameters119862119895 119895 = 1 2 119902 In

this paper we consider the 119898th-order approximation in theform

119865 (120578) asymp 1198650(120578) + 119865

1(120578) + sdot sdot sdot + 119865

119898(120578) (16)

Inserting (14) into (11) we obtain

119871 (F (120578 119901)) + 119873 (F (120578 119901))

= 1198730(1198650(120578)) + 119901119873

1(1198650(120578) 119865

1(120578))

+ 11990121198732(1198650(120578) 119865

1(120578) 119865

2(120578)) + sdot sdot sdot

(17)

where 119873119894(1198650 1198651 119865

119894) is the coefficient of 119901119894 in the expan-

sion of 119871(F) + 119873(F) about the embedding parameter 119901

Substituting (14) and (15) into (11) and equating thecoefficients of like powers of 119901 we obtain the following linearequations

119871 (1198650(120578)) = 0 119861 (119865

0(120578) 119865

1015840

0(120578) 119865

10158401015840

0(120578) ) = 0 (18)

119871 (119865119894(120578)) minus 119871 (119865

119894minus1(120578)) minus

119894

sum

119895=1

119867119895119873119894minus119895(1198650 1198651 119865

119894minus119895) = 0

119861 (119865119894 1198651015840

119894 11986510158401015840

119894 ) = 0 119894 = 1 2 119898 minus 1

(19)

119871 (119865119898(120578)) minus 119871 (119865

119898minus1(120578)) minus

119898minus1

sum

119895=1

119867119895119873119898minus1minus119895

minus 1198671198981198730= 0

119861 (119865119898 1198651015840

119898 11986510158401015840

119898 ) = 0

(20)

At thismoment the mth-order approximate solution (16)depends on the functions119867

1(120578 119862119894)1198672(120578 119862119894) 119867

119898(120578 119862119894)

The parameters1198621 1198622 119862

119902which appear in the expression

of 119867119894 119894 = 1 2 119898 can be identified optimally via

various methodologies such as the least square methodthe Galerkin method and the collocation method Theparameters 119862

1 1198622 119862

119902can be determined for example if

we substitute (16) into (9) such that the residual becomes

119877 (120578 119862119894) = 119871 (119865 (120578 119862

119894)) + 119873(119865 (120578 119862

119894)) 119894 = 1 2 119902

(21)

If 119886 and 119887 are two values from the domain of the problemand 120578

119894isin (119886 119887) 119894 = 1 2 119902 then the residual (21) must

vanish

119877 (1205781 119862119894) = 119877 (120578

2 119862119894) = sdot sdot sdot = 119877 (120578

119902 119862119894) = 0

119894 = 1 2 119902

(22)

with qmdashthe number of parameters 119862119894which appear in the

expression of the functions119867119895(120578) 119895 = 1 2 119898

We remark that our procedure contains the auxiliaryfunctions 119867

1 1198672 which provides us with a simple but

rigorous way to adjust and control convergence of thesolution It must be underlined that it is very important toproperly choose the functions 119867

1 1198672 119867

119898which appear

in the 119898th-order approximation (16) With these parame-ters known the approximate solution is well determinedThe parameters 119862

1 1198622 are namely convergence-control

parameters

4 Application of OHAM toFalkner-Skan Equation

To use the basic ideas of the proposedmethod we choose thelinear operator

119871 (F (120578 119901)) =1205973F (120578 119901)

1205971205783+ 119870

1205972F (120578 119901)

1205971205782 (23)

where 119870 is the unknown parameter at this moment


The nonlinear operator is

119873(F (120578 119901)) = F (120578 119901)1205972F (120578 119901)

1205971205782minus 119870

1205972F (120578 119901)

1205971205782

+ 120573[1 minus (120597F (120578 119901)

120597120578)

2

]

(24)

The boundary conditions are

F (0 119901) = 0120597F (0 119901)

120597120578= 0

120597F (infin 119901)

120597120578= 1

(25)

Equation (18) can be written in the form

119865101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578) = 0

1198650(0) = 0 119865

1015840

0(0) = 0 119865

1015840

0(infin) = 1

(26)

and has the solution

1198650(120578) = 120578 +

119890minus119870120578

minus 1

119870 (27)

From (17) (23) and (24) one obtain the expression

1198730(120578) = minus119870119865

10158401015840

0(120578) + 119865

0(120578) 11986510158401015840

0(120578) + 120573 [1 minus 119865

1015840

0(120578)2

]

(28)

Substituting (27) into (28) we obtain

1198730(120578) = (119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578 (29)

If we consider the first-order approximate solution (119898 =

1) (16) becomes

119865 (120578) = 1198650(120578) + 119865

1(120578) (30)

where 1198651(120578) is obtained from (20)

119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)minus(119865

101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578))=119867

1(120578 119862119894)1198730(120578)

(31)

Substituting (27) and (29) into (31) we obtain the equation

119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)

= 1198671(120578 119862119894) [(119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578]

1198651(0) = 0 119865

1015840

1(0) = 0 119865

1015840

1(infin) = 0

(32)

There are many possibilities to choose the function1198671(120578 119862119894) which appears into (32) The convergence of the

solution 1198651(120578) and consequently the convergence of the

approximate solution 119865(120578) given by (30) depend on theauxiliary function119867

1(120578 119862119894) Basically the shape of119867

1(120578 119862119894)

should follow the term appearing in (29) which is the productof polynomial and exponential functions In general we

try to choose the function 1198671(120578 119862119894) so that the product

1198671(120578 119862119894)1198730(120578) from (31) and 119873

0(120578) would be of the same

form In our paper for example we can consider only thepossibilities

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ sdot sdot sdot + 119862

119902120578119902minus1

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 1198623119890minus119870120578

+ 1198624119890minus2119870120578

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ (1198624+ 1198625120578) 119890minus119870120578

(33)

and so on where 1198621 1198622 are unknown parameters In the

following we have four cases

41 Case 1 If the auxiliary convergence-control function1198671(120578 119862119894) has the form

1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782) 119890minus119870120578

+ 1198628119890minus2119870120578

(34)

then (32) can be written as

119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)

= (2120573 minus 1 minus 1198702) 1198621+ [(2120573 minus 1 minus 119870

2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783+ 11987011986241205784 119890minus119870120578

+ (1 minus 120573)1198621+ (2120573 minus 1 minus 119870

2) 1198625

+ [(1 minus 120573)1198622+ 1198701198625+ (2120573 minus 1 minus 119870

2) 1198626] 120578


2) 1198627] 1205782

+ [(1 minus 120573)1198624+ 1198701198627] 1205783 119890minus2119870120578


2) 1198628

+ [(1 minus 120573)1198626+ 1198701198628] 120578 + (1 minus 120573)119862

71205782 119890minus3119870120578

+ (1 minus 120573)1198628119890minus4119870120578

(35)

Finally using (27) and solving (35) we determine thefirst-order approximate solution given by (30) in the form

119865 (120578) = 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+91198702minus 14120573 minus 4

3611987031198625+541198702minus 92120573 minus 43

21611987041198626

+811198702minus 146120573 minus 97

21611987051198627+481198702minus 69120573 minus 11

43211987031198628

+ [1198624

5119870sdot 1205785+ (

1198623

4119870+2120573 + 7 minus 119870

2

411987021198624) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 2119870

2

311987021198623

+4120573 + 10 minus 2119870

2

11987031198624) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624) sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623

+48120573 + 96 minus 24119870

2

11987051198624) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+10120573 + 5 minus 6119870

2

1211987031198625+49120573 + 41 minus 27119870

2

3611987041198626

+718120573 + 875 minus 378119870

2

21611987051198627

+9120573 + 2 minus 6119870

2

3611987031198628] sdot 119890minus119870120578

+ [(120573 minus 1

411987031198624minus

1

411987021198627) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624minus

1

411987021198626

+1198702minus 5 minus 2120573

411987031198627) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624minus

1

411987021198625

+1198702minus 2120573 minus 3

411987031198626+81198702minus 16120573 minus 25

811987041198627) sdot 120578

+120573 minus 1

411987031198621+120573 minus 1

211987041198622+11120573 minus 11

811987051198623

+39120573 minus 39

811987061198624+1198702minus 2120573 minus 1

411987031198625

+41198702minus 8120573 minus 7

811987041198626+111198702minus 22120573 minus 28

811987051198627] sdot 119890minus2119870120578

+ [

[

120573 minus 1

18119870311986271205782

+ (120573 minus 1

1811987031198626+7120573 minus 7

5411987041198627minus

1

1811987021198628) sdot 120578

+120573 minus 1

1811987031198625+7120573 minus 7

10811987041198626+11120573 minus 11

10811987051198627

+61198702minus 1 minus 12120573

10811987031198628]

]

sdot 119890minus3119870120578

+120573 minus 1

4811987031198628119890minus4119870120578

(36)

42 Case 2 The auxiliary function1198671(120578 119862119894) has the form

1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782) 119890minus119870120578

(37)

In this case (32) becomes

119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783



2) 1198626


2) 1198627] 120578


2) 1198628] 1205782

+ [(1 minus 120573)1198624+ 1198701198628] 1205783+ (1 minus 120573)119862

51205784 119890minus2119870120578

+ [(1 minus 120573)1198626+ (1 minus 120573)119862

7120578 + (1 minus 120573)119862

81205782]

(38)The first-order approximate solution (30) in this case is

obtained from (38) and (27) and can be written as

119865 (120578)

= 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)

43 Case 3 If the auxiliary function1198671(120578 119862119894) has the form

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)

then the first-order approximate solution equation (30) hasthe form

119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)


44 Case 4 In the last case we consider

1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)

such that the first-order approximate solution equation (30)becomes

119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)

5 Numerical Examples

In order to prove the accuracy of the obtained results wewill determine the convergence-control parameters 119862

119894which

appear in (36) (39) (41) and (43) by means of Galerkinmethod Let 119877(120578 119862

119894) be the residual within the approximate

solution 119865(120578) (or 119865(120578)) given by (36) (39) (41) and (43)which satisfies (7)

119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)

Since119877(120578 119862119894) contains the parameters119862

119894 119894 = 1 2 The

parameters can be determined from the conditions

119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)

where119891119894are linear independent functions taken as weighting

functions Equations (36) and (39) contain nine unknown

parameters 119870 and 119862119894 119894 = 1 2 8 and therefore we

consider the following nine weighting functions (119902 = 9)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)

For (41) and (43) which contain the unknownparameters119870 120572 and 119862

119894 119894 = 1 2 9 we consider weighting functions

(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)

In this way the convergence-control parameters 119862119894 119894 =

1 2 are optimally determined and the first-order approx-imate solutions are known for different values of the knownparameter 120573

In what follows we illustrate the accuracy of the OHAMcomparing previously obtained approximate solutions withthe numerical integration results computed by means of theshooting method combined with fourth-order Runge-Kuttamethod using Wolfram Mathematica 60 software Also wewill show that the error of the solutions decreases whenthe number of terms in the auxiliary convergence-controlfunction 119867

1increases For some values of the parameter 120573

we will determine the approximate solutions given by (36)(39) (41) and (43) and with the unknown parameters 120572 119870and 119862

119894obtained from the system given by (45)

Example 1 In the first case we consider that 120573 = 12(a) For (36) and from the system (45) following the pro-

cedure described above the convergence-control parametersare obtained

1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)


Table 1 Comparison between OHAM results given by (49) and numerical solutions for 120573 = 12

120578 119865numerical(120578) 119865OHAM(120578) from (49) Relative error = |119865numerical(120578) minus 119865OHAM(120578)|

0 minus5775724 sdot 10minus25

5551115 sdot 10minus16


45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957

Table 2 Comparison between OHAM results for velocity 1198651015840(120578) obtained from (49) and numerical results for 120573 = 12

120578 1198651015840

numerical(120578) 1198651015840

OHAM(120578) from (49) Relative error = |1198651015840numerical(120578) minus 1198651015840

OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046

and consequently the first-order approximate solution (36)can be written in the form

119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)

In Tables 1 and 2 we present a comparison between thefirst-order approximate solution given by (49) and velocityobtained from (49) respectively with numerical results for

some values of variable 120578 and the corresponding relativeerrors

(b) From (39) obtained by means of the auxiliaryconvergence-control function119867

1given by (37) we obtain the

following results for the parameters

1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)

The first-order approximate solution (39) becomes

119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578





minus13322 sdot 10minus15


45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)

In Tables 3 and 4 we present some values of streamfunction (51) and velocity obtained from (51) respectively fordifferent values of 120578 and the corresponding relative errors

(c) For (41) which depends on the auxiliary convergence-control function119867

1given by (40) we obtain

1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)

Therefore the first-order approximate solution for streamfunction is

119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)

In Tables 5 and 6 we present some values of streamfunction (53) and velocity obtained from (53) respectively







45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196

Table 6 Comparison between OHAM results for velocity 1198651015840

(120578) obtained from (53) and numerical results for 120573 = 12

120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 minus2963953 sdot 10minus20 0 2963953 sdot 10

minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968

for different values of variable 120578 and the correspondingrelative errors

Comparing the results presented in Table 1 with theresults presented in Table 5 and on the other hand the resultspresented in Table 2 with the results presented in Table 6respectively it is clear that the analytical solutions obtainedby our procedure prove to be more accurate along with anincreased number of terms in the auxiliary convergence-control function119867

1

(d) If we consider (43) depending on the auxiliaryconvergence-control function 119867

1given by (42) then from

system (45) we obtain the following results

1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979

The first-order approximate solution for stream function(43) becomes

119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6

Table 9 Comparison between the values of 11986510158401015840(0) obtained by means of OHAM and numerical results for 120573 = 12

Type of equation Equation (49) Equation (51) Equation (53) Equation (55) Numerical11986510158401015840

OHAM(0) 092767733 092763760 092760923 092779335 092768004

In Tables 7 and 8 we present a comparison between thefirst-order approximate solution given by (55) and velocityobtained from (55) respectively with numerical results forsome values of variable 120578 and the corresponding relativeerrors

If we compare the results presented in Tables 3 and 7 andthen the results presented in Tables 4 and 8 respectively wecan arrive at conclusion that the analytical results obtained byOHAM are more accurate along with an increased numberof terms in the auxiliary convergence-control function119867

1 It

is important to establish the value of the shear-stress profile11986510158401015840(0) In Table 9 we present a comparison between the values

of11986510158401015840(0) obtained usingOHAM from (49) (51) (53) and (55)and numerical results for 120573 = 12 Our results are in verygood agreement with the numerical results

Example 2 In this second case we suppose that 120573 = 1(a) For (36) from the system (45) we obtained the values

of the convergence-control parameters

1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818

For these values of the parameters from (36) we obtainedthe first-order approximate solution in the form

119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)

In Tables 10 and 11 we present some values of streamfunction given by (57) and velocity obtained from (57)respectively for different values of variable 120578 Also thecorresponding relative errors are given in these cases

(b) For (39) the system (45) has the solutions

1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)

The first-order approximate solution can be written as

119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)

In Tables 12 and 13 we present some values of streamfunction (59) and velocity obtained from (59) respectivelyfor different values of variable 120578 and the correspondingrelative errors

(c) For (41) with the auxiliary convergence-control func-tion119867

1given by (40) we have

1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)

In Tables 14 and 15 we present some values of streamfunction (61) and velocity obtained from (61) respectively fordifferent values of variable 120578 and the corresponding relativeerrors




0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554

(d) If we have in view (43) with the auxiliary conver-gence-control function119867

1given by (42) then we obtain

1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)

and therefore first-order approximate solution (43) is givenby

119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)

In Tables 16 and 17 we present a comparison between thefirst-order approximate solution given by (63) and velocityobtained from (63) respectively with numerical results andthe corresponding relative errors

If we compare the results presented inTables 10 and 14 andthen the results presented in Tables 11 and 15 we deduce thatthe analytical results obtained by OHAM are more accuratealong with an increased number of terms in the auxiliaryconvergence-control function 119867

1 The same conclusions are

deduced if we compare the results presented in Tables 12and 16 and then the results presented in Tables 13 and 17respectively

In Table 18 we present a comparison between the valuesof 11986510158401015840(0) obtained using OHAM from (57) (59) (61) and(63) and numerical integration results from 120573 = 1 Wecan deduce that the results obtained by means of OHAMare nearly identical with those obtained through numericalintegration




0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769

Example 3 In the last case we consider 120573 = 16(a) For (36) the values of the convergence-control param-

eters are obtained from the system (45)1198621= minus44749746430 119862

2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)

The first-order approximate solution for stream function(36) can be written as

119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)

In Tables 19 and 20 we present some values of thestream function given by (65) and velocity obtained from(65) respectively for different values of variable 120578 Also thecorresponding relative errors are given in these tables

(b) For (39) the convergence-control parametersobtained from the system (45) have the values

1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)

In Tables 21 and 22 we present some values of the streamfunction (67) and velocity obtained from (67) respectivelyand the corresponding relative errors in comparison with thenumerical results


1given by (40) the system (45) has the solutions

1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578

(69)In Tables 23 and 24 we present some values of stream

function (69) and velocity obtained from (69) respectivelyfor different values of variable 120578 and the correspondingrelative errors

(d) If we have in view (43)with the auxiliary convergence-control function 119867

1given by (42) then the convergence-

control parameters obtained from system (45) are1198621= minus99309813061 119862

2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6

In this case the first-order approximate solution forstream function (43) becomes

119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16

Figure 1 Comparison between the approximate solutions (49) (57)and (65) and numerical results with the auxiliary function equation(34) in the cases 120573 = 12 1 and 16 respectively mdashnumerical OHAM solution








45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165

Table 27 Comparison between the values of 11986510158401015840

(0) obtained by means of OHAM and numerical results for 120573 = 16

Type of equation Equation (65) Equation (67) Equation (69) Equation (71) Numerical

119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16

Figure 2 Comparison between the velocity profile obtained from(49) (57) and (65) and numerical results for 120573 = 12 1 and 16respectively mdashnumerical OHAM solution

In Table 27 we present a comparison between the valuesof 11986510158401015840

(0) obtained through OHAM from (65) (67) (69) and(71) and numerical results for 120573 = 16 We can observe thatthe analytical solutions obtained byOHAMare very accuratebeing nearly identical with the numerical results

1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


The accuracy of the obtained results is verified graph-ically in Figures 1ndash8 The approximate solutions obtainedby means of OHAM and with the auxiliary convergence-control functions 119867

1given by (34) (37) (40) and (42) are

compared with numerical integration results for different


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


values of 120573 in Figures 1 3 5 and 7 respectively On theother hand the velocity profile obtained from the corre-sponding approximate solutions is compared with numericalintegration results in Figures 2 4 6 and 8 respectively Inall cases presented in Figures 1ndash8 it is shown that the first-order approximate solutions and the velocity increase with anincrease in the parameter 120573

Just like the above mentioned cases by comparing resultspresented in Tables 18 and 22 and then the results presentedin Tables 19 and 23 we can write that the results obtained byOHAM are more accurate along with an increased numberof terms in the auxiliary convergence-control function 119867

1

Now comparing the results from Tables 20 and 24 and thenthe results fromTables 21 and 25 the conclusions are the same

6 Conclusions

In the present work we proposed an optimal homotopyapproach to obtain approximate analytical solutions fornonlinear differential equation of Falkner-Skan The valid-ity of our procedure called optimal homotopy asymptoticmethod (OHAM) was demonstrated on some representative

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16

Figure 7Comparison between the approximate solutions (55) (63)and (71) and numerical results with the auxiliary function equation(42) in the cases 120573 = 12 1 and 16 respectively mdashnumerical OHAM solution

1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16


examples and very good agreement was found betweenthe approximate analytic results and numerical simulationresultsThe proposed procedure is valid even if the nonlinearequation does not contain any small or large parameter Thebasic equations governing an incompressible fluid subject toa pressure gradient are reduced to a nonlinear differential


equation using similarity variables and are solved bymeans ofOHAMWe examine quantitative effect of parameter120573whichis a measure of the pressure gradient and the relative errors ofapproximate solutions in comparison with numerical results

To solve the equation of Falkner-Skan we used OHAMan approach proposed byMarinca andHerisanu [26ndash28] Forachieving a very accurate solution OHAM ensured a veryrapid convergence after only one iteration Our procedure isa powerful approach for solving nonlinear problems withoutdepending on small parameters

The cornerstone of the validity and flexibility of ourmethod is the choice of the linear operator 119871 and the auxiliaryconvergence-control function 119867

1 The convergence of the

solutions depends on these auxiliary functions and implicitlyon the presence of convergence-control parameters 120572 119870 119862

119894

and 119894 = 1 2 Instead of an infinite series the OHAM searches for only

a few terms and does not need a recurrence formula Theparameters which appear in the composition of the auxiliaryfunctions 119867

1and in the linear operator 119871 are optimally

identified via various methods by rigorously mathematicalpoint of view A large number of parameters in the auxiliaryfunctions 119867

1lead to a better accuracy of the results In all

cases presented in this paper for different values of theparameter 120573 we obtain an excellent agreement of the first-order approximate solutions

Also we obtain very good results by OHAM for differentrepresentative values of parameter 120573 for shear-stress profiles11986510158401015840

(0) of the Falkner-Skan equation in comparison withthe results obtained via numerical integration It is worthmentioning that the proposedmethod is straightforward andconcise and can be applied to other nonlinear problems

It is interesting to remark that a large number of parame-ters119862

119894in the auxiliary convergence-control functions119867

1lead

to a better accuracy of the results (for the stream function andvelocity) On the other hand results obtained by OHAM aremore accurate along with increased values of the parameter120573

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] J de Vicente Viscoelsticitymdashfrom Theory to Biological Applica-tions 2012

[2] V M Falkner and S W Skan ldquoSome approximate solutions ofthe boundary layer equationsrdquo Philosophical Magazine vol 12pp 865ndash816 1931

[3] D R Hartree ldquoOn the equation occurring in Falkner and Skanrsquosapproximate treatment of the equations of the boundary layerrdquoProceedings of the Cambridge Philosophical Society vol 33 pp223ndash239 1937

[4] K Stewartson ldquoFurther solutions of the Falkner-Skan equa-tionrdquoProceedings of the Cambridge Philosophical Society vol 50pp 454ndash465 1954

[5] S P Hastings ldquoReversed flow solutions of the Falkner-Skanequationrdquo SIAM Journal of Applied Mathematics vol 22 no 2pp 329ndash334 1972

[6] E F F Botta F JHut andA E PVeldman ldquoThe role of periodicsolutions in the Falkner-Skan problem for 120582 ge 0rdquo Journal ofEngineering Mathematics vol 20 no 1 pp 81ndash93 1986

[7] K A Yih ldquoUniform suctionblowing effect on forced convec-tion about a wedge uniformheat fluxrdquoActaMechanica vol 128no 3-4 pp 173ndash181 1998

[8] A Asaithambi ldquoA finite differencemethod for the Falkner-Skanequationrdquo Applied Mathematics and Computation vol 92 no23 pp 135ndash141 1998

[9] M B Zaturska andW N Banks ldquoA new solution branch of theFalkner-Skan equationrdquo Acta Mechanica vol 152 no 1ndash4 pp197ndash201 2001

[10] B L Kuo ldquoApplication of the differential transformationmethod to the solutions of Falkner-Skan wedge flowrdquo ActaMechanica vol 164 no 3-4 pp 161ndash174 2003

[11] N S Elgazery ldquoNumerical solution for the Falkner-Skan equa-tionrdquo Chaos Solitons and Fractals vol 35 no 4 pp 738ndash7462008

[12] E Alizadeh M Farhadi K Sedighi H R Ebrahimi-Kebriaand A Ghafourian ldquoSolution of the Falkner-Skan equation forwedge by Adomian Decomposition Methodrdquo CommunicationsinNonlinear Science andNumerical Simulation vol 14 no 3 pp724ndash733 2009

[13] S Abbasbandy and T Hayat ldquoSolution of the MHD Falkner-Skan flow by Hankel-Pade methodrdquo Physics Letters A GeneralAtomic and Solid State Physics vol 373 no 7 pp 731ndash734 2009

[14] S Abbasbandy and T Hayat ldquoSolution of the MHD Falkner-Skan flow by homotopy analysis methodrdquo Communications inNonlinear Science and Numerical Simulation vol 14 no 9-10pp 3591ndash3598 2009

[15] S Bernhard S Mohlenkamp and A Tilgner ldquoTransientintegral boundary layer method to calculate the translesionalpressure drop and the fractional flow reserve in myocardialbridgesrdquo BioMedical Engineering Online vol 5 article 42 2006

[16] A Pirkhedri H H S Javadi K Parand N Fatahi and SLotfi ldquoSolving MHD Falkner-Skan boundary-layer equationusing collocation method based on rational Legendre functionwith transformedHermite-Gauss noderdquoWorld Applied SciencesJournal vol 13 no 10 pp 2224ndash2230 2011

[17] K Ahmad R Nazar and I Pop ldquoFalkner-Skan solutionfor gravity-driven film flow of a micropolar fluidrdquo SainsMalaysiana vol 40 no 11 pp 1291ndash1296 2011

[18] M Lakestani ldquoNumerical solution for the Falkner-Skan equa-tion using Chebyshev cardinal functionsrdquo Acta UniversitasApulensis vol 27 pp 229ndash238 2011

[19] B Y Yun ldquoNew approximate analytical solutions of the Falkner-Skan equationrdquo Journal of Applied Mathematics vol 2012Article ID 170802 12 pages 2012

[20] F A Hendi and M Hussain ldquoAnalytic solution for MHDFalkner-Skan flow over a porous surfacerdquo Journal of AppliedMathematics vol 2012 Article ID 123185 9 pages 2012

[21] G Adomian ldquoA review of the decomposition method inapplied mathematicsrdquo Journal of Mathematical Analysis andApplications vol 135 no 2 pp 501ndash544 1988

[22] Y K Cheung S H Chen and S L Lau ldquoAmodified Lindstedt-Poincare method for certain strongly non-linear oscillatorsrdquoInternational Journal of Non-Linear Mechanics vol 26 no 3-4pp 367ndash378 1991


[23] F O Zengin M O Kaya and S A Demirbag ldquoApplicationof parameter-expansion method to nonlinear oscillators withdiscontinuitiesrdquo International Journal of Nonlinear Sciences andNumerical Simulation vol 9 no 3 pp 267ndash270 2008

[24] V Marinca and N Herisanu ldquoOptimal variational method fortruly nonlinear oscillatorsrdquo Journal of AppliedMathematics vol2012 Article ID 620267 10 pages 2012

[25] N Herisanu and V Marinca ldquoOptimal homotopy perturbationmethod for non-conservative dynamical system of a rotatingelectrical machinerdquo Zeitschrift fur Naturforschung vol 670 pp509ndash516 2012

[26] V Marinca and N Herisanu Nonlinear Dynamical Systems inEngineeringmdashSome Approximate Approaches Springer BerlinGermany 2011

[27] V Marinca N Herisanu C Bota and B Marinca ldquoAn optimalhomotopy asymptotic method applied to the steady flow of afourth-grade fluid past a porous platerdquo Applied MathematicsLetters vol 22 no 2 pp 245ndash251 2009

[28] V Marinca and N Herisanu ldquoDetermination of periodicsolutions for the motion of a particle on a rotating parabola bymeans of the optimal homotopy asymptotic methodrdquo Journal ofSound and Vibration vol 329 no 9 pp 1450ndash1459 2010

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


[12] byAlizadeh et al to find an analytical solution in the formof infinite power series Magnetohydrodynamic effects onthe Falkner-Skan wedge flow are studied by Abbasbandy andHayat in [13]The same authors usedHankel-Pade and homo-topy analysis method for the derivation of the solutions [14]From a fluidmechanical point of view the pathophysiologicalsituation in myocardical bridges involves fluid flow in atime dependent flow geometry caused by contracting cardiacmuscles overlying an intramural segment of the coronaryartery A boundary-layer model for the calculation of thepressure drop and flow separation is presented in [15] underthe assumption that the idealized flow through a constrictionis given by near equilibrium velocity profiles of the Falkner-Skan-Cooke family the evolution of the boundary-layer isobtained by the simultaneous solution of the Falkner-Skanequation and the transient non-Karman integral momentumequation

Pirkhedri et al [16] developed a numerical techniquetransforming the governing partial differential equation intoa nonlinear third-order boundary value problemby similarityvariables and then solved it by the rational Legendre collo-cation method It used transformed Hermite-Gauss nodesas interpolation points The steady Falkner-Skan solution forgravity-driven film flow of micropolar fluid is investigated in[17] The ordinary differential equations are solved numeri-cally using an implicit finite difference scheme known as theKeller-box method In [18] Lakestani truncated the semi-infinite physical domain of the problem to a finite domainexpanding the required approximate solution as the elementsof Chebyshev cardinal functions Yun proposed in [19] aniterative method for solving the Falkner-Skan equation in theform of polynomial series without requiring any differenti-ations or integrations of the previous iterate solutions Theauthor suggests a correction method which is compared withthe successive differences of the iterations In [20] Hendi andHussain considered Falkner-Skan flow over a porous surfacetaking into account the case of uniform suctionblowingStream function formulation and suitable transformationsreduce the arising problem to ordinary differential equationwhich has been solved by homotopy analysis method

In science and engineering there exist a lot of nonlineardifferential equations and even strongly nonlinear problemswhich are still very difficult to solve analytically by using tra-ditional methods Many methods exist for approximating thesolutions of nonlinear problems for example the Adomiandecompositionmethod [21] themodifiedLindstedt-Poincaremethod [22] the parameter-expansion method [23] optimalvariational method [24] optimal homotopy perturbationmethod [25] and so on [26]

The aim of the present paper is to propose an accurateapproach to Falkner-Skan equation using an analytical tech-nique namely optimal homotopy asymptotic method [26ndash28]

The validity of our procedure which does not imply thepresence of a small parameter in the equation is based onthe construction and determination of the auxiliary functionscombined with a convenient way to optimally control theconvergence of the solution The efficiency of the proposedprocedure is proved while an accurate solution is explicitly

analytically obtained in an iterative way after only oneiteration

2 The Governing Equation

The two-dimensional laminar boundary-layer equations ofan incompressible fluid subject to a pressure gradient are[2 3 9 12]

119906120597119906

120597119909+ V

120597119906

120597119910= minus

1

1205881199011015840+ ]

1205972119906

1205971199102 (1)

120597119906

120597119909+120597V120597119910

= 0 (2)

where 1199011015840 is the pressure gradient 1199011015840 = minus120588119880(120597119880120597119909) 119906 isthe streamwise velocity in the direction of the fluid flow Vis the velocity in the direction normal to 119906 ] is the constantkinematic viscosity and119880(119909) is the velocity at the edge of theboundary-layer which obeys the power-law relation 119880(119909) =119886119909119898 (119909 gt 0) where 119886 is the mean stream velocity and 119898 is

a constant The relevant boundary conditions for fixed plateare

119910 = 0 119906 = 0 V = 0 119906 997888rarr 119886 as 119910 997888rarr infin (3)

A stream function 120595(119909 119910) is introduced such that

119906 =120597120595

120597119910 V = minus

120597120595

120597119909 (4)

Equation (2) of continuity is satisfied identically Themomentum equation (1) becomes

120597120595

120597119910

1205972120595

120597119909120597119910minus120597120595

120597119909

1205972120595

1205971199102= 119880

120597119880

120597119909+ ]

1205973120595

1205971199103 (5)

Integrating (5) and using similarity variable yield

120595 = 119909(1+119898)2

radic2]1198861 + 119898

119865 (120578)

120578 =119910

119909(1minus119898)2radic(1 + 119898) 119886

2]

(6)

Substituting (6) into (5) gives the equation of Falkner-Skan in the form

119865101584010158401015840(120578) + 119865 (120578) 119865

10158401015840(120578) + 120573 (1 minus 119865

1015840(120578)2

) = 0 (7)

with the initial and boundary conditions

119865 (0) = 0 1198651015840

(0) = 0 1198651015840

(infin) = 0 (8)

where 120573 = 2119898(119898 + 1) is a measure of the pressure gradientand prime denotes derivative with respect to 120578




119871 (119865 (120578)) + 119873 (119865 (120578)) = 0 (9)


119861 (119865 1198651015840 11986510158401015840 ) = 0 (10)



(1 minus 119901) 119871 (F (120578 119901))

= 119867 (120578 119901) [119871 (F (120578 119901)) + 119873 (F (120578 119901))]

(11)


119861(F (120578 119901) 120597F (120578 119901)

1205971205781205972F (120578 119901)

1205971205782 ) = 0 (12)




F (120578 0) = 1198650(120578) F (120578 1) = 119865 (120578) (13)


F (120578 119901) = 1198650(120578) + 119901119865

1(120578) + 119901

21198652(120578) + sdot sdot sdot (14)


119867(120578 119901) = 1199011198671(120578 119862119895) + 11990121198672(120578 119862119895) + sdot sdot sdot (15)




119865 (120578) asymp 1198650(120578) + 119865

1(120578) + sdot sdot sdot + 119865

119898(120578) (16)


119871 (F (120578 119901)) + 119873 (F (120578 119901))

= 1198730(1198650(120578)) + 119901119873

1(1198650(120578) 119865

1(120578))

+ 11990121198732(1198650(120578) 119865

1(120578) 119865


(17)

where 119873119894(1198650 1198651 119865




119871 (1198650(120578)) = 0 119861 (119865

0(120578) 119865

1015840

0(120578) 119865

10158401015840

0(120578) ) = 0 (18)

119871 (119865119894(120578)) minus 119871 (119865

119894minus1(120578)) minus

119894

sum

119895=1

119867119895119873119894minus119895(1198650 1198651 119865

119894minus119895) = 0

119861 (119865119894 1198651015840

119894 11986510158401015840

119894 ) = 0 119894 = 1 2 119898 minus 1

(19)

119871 (119865119898(120578)) minus 119871 (119865

119898minus1(120578)) minus

119898minus1

sum

119895=1

119867119895119873119898minus1minus119895

minus 1198671198981198730= 0

119861 (119865119898 1198651015840

119898 11986510158401015840

119898 ) = 0

(20)


1(120578 119862119894)1198672(120578 119862119894) 119867

119898(120578 119862119894)

The parameters1198621 1198622 119862




1 1198622 119862



119877 (120578 119862119894) = 119871 (119865 (120578 119862

119894)) + 119873(119865 (120578 119862

119894)) 119894 = 1 2 119902

(21)



vanish

119877 (1205781 119862119894) = 119877 (120578

2 119862119894) = sdot sdot sdot = 119877 (120578

119902 119862119894) = 0

119894 = 1 2 119902

(22)






1 1198672 119867

119898which appear



parameters



119871 (F (120578 119901)) =1205973F (120578 119901)

1205971205783+ 119870

1205972F (120578 119901)

1205971205782 (23)




119873(F (120578 119901)) = F (120578 119901)1205972F (120578 119901)

1205971205782minus 119870

1205972F (120578 119901)

1205971205782

+ 120573[1 minus (120597F (120578 119901)

120597120578)

2

]

(24)


F (0 119901) = 0120597F (0 119901)

120597120578= 0

120597F (infin 119901)

120597120578= 1

(25)


119865101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578) = 0

1198650(0) = 0 119865

1015840

0(0) = 0 119865

1015840

0(infin) = 1

(26)


1198650(120578) = 120578 +

119890minus119870120578

minus 1

119870 (27)


1198730(120578) = minus119870119865

10158401015840

0(120578) + 119865

0(120578) 11986510158401015840

0(120578) + 120573 [1 minus 119865

1015840

0(120578)2

]

(28)


1198730(120578) = (119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578 (29)


1) (16) becomes

119865 (120578) = 1198650(120578) + 119865

1(120578) (30)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)minus(119865

101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578))=119867

1(120578 119862119894)1198730(120578)

(31)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)

= 1198671(120578 119862119894) [(119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578]

1198651(0) = 0 119865

1015840

1(0) = 0 119865

1015840

1(infin) = 0

(32)





1(120578 119862119894)



1198671(120578 119862119894)1198730(120578) from (31) and 119873



1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ sdot sdot sdot + 119862

119902120578119902minus1

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 1198623119890minus119870120578

+ 1198624119890minus2119870120578

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ (1198624+ 1198625120578) 119890minus119870120578

(33)




1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782) 119890minus119870120578

+ 1198628119890minus2119870120578

(34)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782



2) 1198625


2) 1198626] 120578


2) 1198627] 1205782

+ [(1 minus 120573)1198624+ 1198701198627] 1205783 119890minus2119870120578


2) 1198628

+ [(1 minus 120573)1198626+ 1198701198628] 120578 + (1 minus 120573)119862

71205782 119890minus3119870120578

+ (1 minus 120573)1198628119890minus4119870120578

(35)


119865 (120578) = 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+91198702minus 14120573 minus 4

3611987031198625+541198702minus 92120573 minus 43

21611987041198626

+811198702minus 146120573 minus 97

21611987051198627+481198702minus 69120573 minus 11

43211987031198628

+ [1198624

5119870sdot 1205785+ (

1198623

4119870+2120573 + 7 minus 119870

2

411987021198624) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 2119870

2

311987021198623

+4120573 + 10 minus 2119870

2

11987031198624) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624) sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623

+48120573 + 96 minus 24119870

2

11987051198624) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+10120573 + 5 minus 6119870

2

1211987031198625+49120573 + 41 minus 27119870

2

3611987041198626

+718120573 + 875 minus 378119870

2

21611987051198627

+9120573 + 2 minus 6119870

2

3611987031198628] sdot 119890minus119870120578

+ [(120573 minus 1

411987031198624minus

1

411987021198627) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624minus

1

411987021198626

+1198702minus 5 minus 2120573

411987031198627) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624minus

1

411987021198625

+1198702minus 2120573 minus 3

411987031198626+81198702minus 16120573 minus 25

811987041198627) sdot 120578

+120573 minus 1

411987031198621+120573 minus 1

211987041198622+11120573 minus 11

811987051198623

+39120573 minus 39

811987061198624+1198702minus 2120573 minus 1

411987031198625

+41198702minus 8120573 minus 7

811987041198626+111198702minus 22120573 minus 28

811987051198627] sdot 119890minus2119870120578

+ [

[

120573 minus 1

18119870311986271205782

+ (120573 minus 1

1811987031198626+7120573 minus 7

5411987041198627minus

1

1811987021198628) sdot 120578

+120573 minus 1

1811987031198625+7120573 minus 7

10811987041198626+11120573 minus 11

10811987051198627

+61198702minus 1 minus 12120573

10811987031198628]

]

sdot 119890minus3119870120578

+120573 minus 1

4811987031198628119890minus4119870120578

(36)


1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782) 119890minus119870120578

(37)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783



2) 1198626


2) 1198627] 120578


2) 1198628] 1205782

+ [(1 minus 120573)1198624+ 1198701198628] 1205783+ (1 minus 120573)119862

51205784 119890minus2119870120578

+ [(1 minus 120573)1198626+ (1 minus 120573)119862

7120578 + (1 minus 120573)119862

81205782]



119865 (120578)

= 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)


1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)



1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119871 (119865 (120578)) + 119873 (119865 (120578)) = 0 (9)


119861 (119865 1198651015840 11986510158401015840 ) = 0 (10)



(1 minus 119901) 119871 (F (120578 119901))

= 119867 (120578 119901) [119871 (F (120578 119901)) + 119873 (F (120578 119901))]

(11)


119861(F (120578 119901) 120597F (120578 119901)

1205971205781205972F (120578 119901)

1205971205782 ) = 0 (12)




F (120578 0) = 1198650(120578) F (120578 1) = 119865 (120578) (13)


F (120578 119901) = 1198650(120578) + 119901119865

1(120578) + 119901

21198652(120578) + sdot sdot sdot (14)


119867(120578 119901) = 1199011198671(120578 119862119895) + 11990121198672(120578 119862119895) + sdot sdot sdot (15)




119865 (120578) asymp 1198650(120578) + 119865

1(120578) + sdot sdot sdot + 119865

119898(120578) (16)


119871 (F (120578 119901)) + 119873 (F (120578 119901))

= 1198730(1198650(120578)) + 119901119873

1(1198650(120578) 119865

1(120578))

+ 11990121198732(1198650(120578) 119865

1(120578) 119865


(17)

where 119873119894(1198650 1198651 119865




119871 (1198650(120578)) = 0 119861 (119865

0(120578) 119865

1015840

0(120578) 119865

10158401015840

0(120578) ) = 0 (18)

119871 (119865119894(120578)) minus 119871 (119865

119894minus1(120578)) minus

119894

sum

119895=1

119867119895119873119894minus119895(1198650 1198651 119865

119894minus119895) = 0

119861 (119865119894 1198651015840

119894 11986510158401015840

119894 ) = 0 119894 = 1 2 119898 minus 1

(19)

119871 (119865119898(120578)) minus 119871 (119865

119898minus1(120578)) minus

119898minus1

sum

119895=1

119867119895119873119898minus1minus119895

minus 1198671198981198730= 0

119861 (119865119898 1198651015840

119898 11986510158401015840

119898 ) = 0

(20)


1(120578 119862119894)1198672(120578 119862119894) 119867

119898(120578 119862119894)

The parameters1198621 1198622 119862




1 1198622 119862



119877 (120578 119862119894) = 119871 (119865 (120578 119862

119894)) + 119873(119865 (120578 119862

119894)) 119894 = 1 2 119902

(21)



vanish

119877 (1205781 119862119894) = 119877 (120578

2 119862119894) = sdot sdot sdot = 119877 (120578

119902 119862119894) = 0

119894 = 1 2 119902

(22)






1 1198672 119867

119898which appear



parameters



119871 (F (120578 119901)) =1205973F (120578 119901)

1205971205783+ 119870

1205972F (120578 119901)

1205971205782 (23)




119873(F (120578 119901)) = F (120578 119901)1205972F (120578 119901)

1205971205782minus 119870

1205972F (120578 119901)

1205971205782

+ 120573[1 minus (120597F (120578 119901)

120597120578)

2

]

(24)


F (0 119901) = 0120597F (0 119901)

120597120578= 0

120597F (infin 119901)

120597120578= 1

(25)


119865101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578) = 0

1198650(0) = 0 119865

1015840

0(0) = 0 119865

1015840

0(infin) = 1

(26)


1198650(120578) = 120578 +

119890minus119870120578

minus 1

119870 (27)


1198730(120578) = minus119870119865

10158401015840

0(120578) + 119865

0(120578) 11986510158401015840

0(120578) + 120573 [1 minus 119865

1015840

0(120578)2

]

(28)


1198730(120578) = (119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578 (29)


1) (16) becomes

119865 (120578) = 1198650(120578) + 119865

1(120578) (30)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)minus(119865

101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578))=119867

1(120578 119862119894)1198730(120578)

(31)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)

= 1198671(120578 119862119894) [(119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578]

1198651(0) = 0 119865

1015840

1(0) = 0 119865

1015840

1(infin) = 0

(32)





1(120578 119862119894)



1198671(120578 119862119894)1198730(120578) from (31) and 119873



1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ sdot sdot sdot + 119862

119902120578119902minus1

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 1198623119890minus119870120578

+ 1198624119890minus2119870120578

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ (1198624+ 1198625120578) 119890minus119870120578

(33)




1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782) 119890minus119870120578

+ 1198628119890minus2119870120578

(34)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782



2) 1198625


2) 1198626] 120578


2) 1198627] 1205782

+ [(1 minus 120573)1198624+ 1198701198627] 1205783 119890minus2119870120578


2) 1198628

+ [(1 minus 120573)1198626+ 1198701198628] 120578 + (1 minus 120573)119862

71205782 119890minus3119870120578

+ (1 minus 120573)1198628119890minus4119870120578

(35)


119865 (120578) = 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+91198702minus 14120573 minus 4

3611987031198625+541198702minus 92120573 minus 43

21611987041198626

+811198702minus 146120573 minus 97

21611987051198627+481198702minus 69120573 minus 11

43211987031198628

+ [1198624

5119870sdot 1205785+ (

1198623

4119870+2120573 + 7 minus 119870

2

411987021198624) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 2119870

2

311987021198623

+4120573 + 10 minus 2119870

2

11987031198624) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624) sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623

+48120573 + 96 minus 24119870

2

11987051198624) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+10120573 + 5 minus 6119870

2

1211987031198625+49120573 + 41 minus 27119870

2

3611987041198626

+718120573 + 875 minus 378119870

2

21611987051198627

+9120573 + 2 minus 6119870

2

3611987031198628] sdot 119890minus119870120578

+ [(120573 minus 1

411987031198624minus

1

411987021198627) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624minus

1

411987021198626

+1198702minus 5 minus 2120573

411987031198627) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624minus

1

411987021198625

+1198702minus 2120573 minus 3

411987031198626+81198702minus 16120573 minus 25

811987041198627) sdot 120578

+120573 minus 1

411987031198621+120573 minus 1

211987041198622+11120573 minus 11

811987051198623

+39120573 minus 39

811987061198624+1198702minus 2120573 minus 1

411987031198625

+41198702minus 8120573 minus 7

811987041198626+111198702minus 22120573 minus 28

811987051198627] sdot 119890minus2119870120578

+ [

[

120573 minus 1

18119870311986271205782

+ (120573 minus 1

1811987031198626+7120573 minus 7

5411987041198627minus

1

1811987021198628) sdot 120578

+120573 minus 1

1811987031198625+7120573 minus 7

10811987041198626+11120573 minus 11

10811987051198627

+61198702minus 1 minus 12120573

10811987031198628]

]

sdot 119890minus3119870120578

+120573 minus 1

4811987031198628119890minus4119870120578

(36)


1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782) 119890minus119870120578

(37)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783



2) 1198626


2) 1198627] 120578


2) 1198628] 1205782

+ [(1 minus 120573)1198624+ 1198701198628] 1205783+ (1 minus 120573)119862

51205784 119890minus2119870120578

+ [(1 minus 120573)1198626+ (1 minus 120573)119862

7120578 + (1 minus 120573)119862

81205782]



119865 (120578)

= 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)


1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)



1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119873(F (120578 119901)) = F (120578 119901)1205972F (120578 119901)

1205971205782minus 119870

1205972F (120578 119901)

1205971205782

+ 120573[1 minus (120597F (120578 119901)

120597120578)

2

]

(24)


F (0 119901) = 0120597F (0 119901)

120597120578= 0

120597F (infin 119901)

120597120578= 1

(25)


119865101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578) = 0

1198650(0) = 0 119865

1015840

0(0) = 0 119865

1015840

0(infin) = 1

(26)


1198650(120578) = 120578 +

119890minus119870120578

minus 1

119870 (27)


1198730(120578) = minus119870119865

10158401015840

0(120578) + 119865

0(120578) 11986510158401015840

0(120578) + 120573 [1 minus 119865

1015840

0(120578)2

]

(28)


1198730(120578) = (119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578 (29)


1) (16) becomes

119865 (120578) = 1198650(120578) + 119865

1(120578) (30)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)minus(119865

101584010158401015840

0(120578) + 119870119865

10158401015840

0(120578))=119867

1(120578 119862119894)1198730(120578)

(31)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)

= 1198671(120578 119862119894) [(119870120578 + 2120573 minus 1 minus 119870) 119890

minus119870120578+ (1 minus 120573) 119890

minus2119870120578]

1198651(0) = 0 119865

1015840

1(0) = 0 119865

1015840

1(infin) = 0

(32)





1(120578 119862119894)



1198671(120578 119862119894)1198730(120578) from (31) and 119873



1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ sdot sdot sdot + 119862

119902120578119902minus1

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 1198623119890minus119870120578

+ 1198624119890minus2119870120578

1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ (1198624+ 1198625120578) 119890minus119870120578

(33)




1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782) 119890minus119870120578

+ 1198628119890minus2119870120578

(34)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782



2) 1198625


2) 1198626] 120578


2) 1198627] 1205782

+ [(1 minus 120573)1198624+ 1198701198627] 1205783 119890minus2119870120578


2) 1198628

+ [(1 minus 120573)1198626+ 1198701198628] 120578 + (1 minus 120573)119862

71205782 119890minus3119870120578

+ (1 minus 120573)1198628119890minus4119870120578

(35)


119865 (120578) = 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+91198702minus 14120573 minus 4

3611987031198625+541198702minus 92120573 minus 43

21611987041198626

+811198702minus 146120573 minus 97

21611987051198627+481198702minus 69120573 minus 11

43211987031198628

+ [1198624

5119870sdot 1205785+ (

1198623

4119870+2120573 + 7 minus 119870

2

411987021198624) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 2119870

2

311987021198623

+4120573 + 10 minus 2119870

2

11987031198624) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624) sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623

+48120573 + 96 minus 24119870

2

11987051198624) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+10120573 + 5 minus 6119870

2

1211987031198625+49120573 + 41 minus 27119870

2

3611987041198626

+718120573 + 875 minus 378119870

2

21611987051198627

+9120573 + 2 minus 6119870

2

3611987031198628] sdot 119890minus119870120578

+ [(120573 minus 1

411987031198624minus

1

411987021198627) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624minus

1

411987021198626

+1198702minus 5 minus 2120573

411987031198627) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624minus

1

411987021198625

+1198702minus 2120573 minus 3

411987031198626+81198702minus 16120573 minus 25

811987041198627) sdot 120578

+120573 minus 1

411987031198621+120573 minus 1

211987041198622+11120573 minus 11

811987051198623

+39120573 minus 39

811987061198624+1198702minus 2120573 minus 1

411987031198625

+41198702minus 8120573 minus 7

811987041198626+111198702minus 22120573 minus 28

811987051198627] sdot 119890minus2119870120578

+ [

[

120573 minus 1

18119870311986271205782

+ (120573 minus 1

1811987031198626+7120573 minus 7

5411987041198627minus

1

1811987021198628) sdot 120578

+120573 minus 1

1811987031198625+7120573 minus 7

10811987041198626+11120573 minus 11

10811987051198627

+61198702minus 1 minus 12120573

10811987031198628]

]

sdot 119890minus3119870120578

+120573 minus 1

4811987031198628119890minus4119870120578

(36)


1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782) 119890minus119870120578

(37)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783



2) 1198626


2) 1198627] 120578


2) 1198628] 1205782

+ [(1 minus 120573)1198624+ 1198701198628] 1205783+ (1 minus 120573)119862

51205784 119890minus2119870120578

+ [(1 minus 120573)1198626+ (1 minus 120573)119862

7120578 + (1 minus 120573)119862

81205782]



119865 (120578)

= 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)


1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)



1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










+91198702minus 14120573 minus 4

3611987031198625+541198702minus 92120573 minus 43

21611987041198626

+811198702minus 146120573 minus 97

21611987051198627+481198702minus 69120573 minus 11

43211987031198628

+ [1198624

5119870sdot 1205785+ (

1198623

4119870+2120573 + 7 minus 119870

2

411987021198624) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 2119870

2

311987021198623

+4120573 + 10 minus 2119870

2

11987031198624) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624) sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623

+48120573 + 96 minus 24119870

2

11987051198624) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+10120573 + 5 minus 6119870

2

1211987031198625+49120573 + 41 minus 27119870

2

3611987041198626

+718120573 + 875 minus 378119870

2

21611987051198627

+9120573 + 2 minus 6119870

2

3611987031198628] sdot 119890minus119870120578

+ [(120573 minus 1

411987031198624minus

1

411987021198627) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624minus

1

411987021198626

+1198702minus 5 minus 2120573

411987031198627) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624minus

1

411987021198625

+1198702minus 2120573 minus 3

411987031198626+81198702minus 16120573 minus 25

811987041198627) sdot 120578

+120573 minus 1

411987031198621+120573 minus 1

211987041198622+11120573 minus 11

811987051198623

+39120573 minus 39

811987061198624+1198702minus 2120573 minus 1

411987031198625

+41198702minus 8120573 minus 7

811987041198626+111198702minus 22120573 minus 28

811987051198627] sdot 119890minus2119870120578

+ [

[

120573 minus 1

18119870311986271205782

+ (120573 minus 1

1811987031198626+7120573 minus 7

5411987041198627minus

1

1811987021198628) sdot 120578

+120573 minus 1

1811987031198625+7120573 minus 7

10811987041198626+11120573 minus 11

10811987051198627

+61198702minus 1 minus 12120573

10811987031198628]

]

sdot 119890minus3119870120578

+120573 minus 1

4811987031198628119890minus4119870120578

(36)


1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782) 119890minus119870120578

(37)


119865101584010158401015840

1(120578) + 119870119865

10158401015840

1(120578)


2) 1198622+ 1198701198621] 120578

+ [(2120573 minus 1 minus 1198702) 1198623+ 1198701198622] 1205782

+ [(2120573 minus 1 minus 1198702) 1198624+ 1198701198623] 1205783



2) 1198626


2) 1198627] 120578


2) 1198628] 1205782

+ [(1 minus 120573)1198624+ 1198701198628] 1205783+ (1 minus 120573)119862

51205784 119890minus2119870120578

+ [(1 minus 120573)1198626+ (1 minus 120573)119862

7120578 + (1 minus 120573)119862

81205782]



119865 (120578)

= 120578 minus1

119870+41198702minus 7120573 minus 5

411987031198621+81198702minus 15120573 minus 17

411987041198622

+481198702minus 93120573 minus 147

811987051198623+961198702minus 189120573 minus 387

411987061198624


+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)


1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)



1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










+9601198702minus 1935120573 minus 4785

811987071198625+91198702minus 14120573 minus 4

3611987031198626

+541198702minus 92120573 minus 43

21611987041198627+811198702minus 146120573 minus 97

21611987051198628

+ [1198625

61198701205786+ (

1198624

5119870+2120573 + 9 minus 119870

2

911987021198625) sdot 1205785

+ (1198623

4119870+2120573 + 7 minus 119870

2

411987021198624+4120573 + 13 minus 2119870

2

11987031198625) sdot 1205784

+ (1198622

3119870+2120573 + 5 minus 119870

2

311987021198623+4120573 + 10 minus 2119870

2

11987031198624

+24120573 + 68 minus 12119870

2

11987041198625) sdot 1205783

+ (1198621

2119870+2120573 + 3 minus 119870

2

211987021198622+4120573 + 7 minus 2119870

2

11987031198623

+18120573 + 39 minus 9119870

2

11987041198624+96120573 + 252 minus 48119870

2

11987051198625)sdot 1205782

+ (2120573 + 1 minus 119870

2

11987021198621+4120573 + 4 minus 2119870

2

11987031198622

+12120573 + 18 minus 6119870

2

11987041198623+48120573 + 96 minus 24119870

2

11987051198624

+240120573 + 600 minus 120119870

2

11987061198625) sdot 120578

+1

119870+3120573 + 3 minus 2119870

2

211987031198621+13120573 + 19 minus 8119870

2

411987041198622

+41120573 + 79 minus 24119870

2

411987051198623+339120573 + 813 minus 192119870

2

811987061198624

+1053120573 + 2307 minus 480119870

2

411987071198625+10120573 + 5 minus 6119870

2

1211987031198626

+49120573 + 41 minus 27119870

2

3611987041198627

+718120573 + 875 minus 378119870

2

21611987051198628] sdot 119890minus119870120578

+ [120573 minus 1

4119870311986251205784+ (

120573 minus 1

411987031198624minus2120573 minus 2

11987041198625minus

1

411987021198628) sdot 1205783

+ (120573 minus 1

411987031198623+3120573 minus 3

211987041198624+33120573 minus 33

411987051198625minus

1

411987021198627

+2120573 minus 7 minus 119870

2

411987031198628) sdot 1205782

+ (120573 minus 1

411987031198622+120573 minus 1

11987041198623+33120573 minus 33

811987051198624

+39 minus 39120573

211987061198625minus

1

411987021198626+1198702minus 2120573 minus 3

411987031198627

+81198702minus 16120573 minus 25

811987041198628) sdot 120578 +

120573 minus 1

411987031198621+120573 minus 1

211987041198622

+11120573 minus 11

811987051198623+39120573 minus 39

811987061198624+171120573 minus 171

811987071198625

+1198702minus 2120573 minus 1

411987031198626+41198702minus 8120573 minus 7

811987041198627

+111198702minus 22120573 minus 28

811987051198628] sdot 119890minus2119870120578

+ [120573 minus 1

18119870311986281205782+ (

120573 minus 1

1811987031198627+7120573 minus 7

5411987041198628) sdot 120578

+120573 minus 1

1811987031198626+7120573 minus 7

10811987041198627+11120573 minus 11

10811987051198628] sdot 119890minus3119870120578

(39)


1198671(120578 119862119894) = 119862

1+ 1198622120578 + 11986231205782+ 11986241205783

+ (1198625+ 1198626120578 + 11986271205782+ 11986291205783) 119890minus119870120578

+ 1198628119890minus2119870120578

(40)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+ ( minus1

411987021205784+1198702minus 7 minus 2120573

411987031205783

+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782

+11120573 minus 11

361198705120578 +

131120573 minus 131

6481198706) 119890minus3119870120578

]

(41)

where 119865(120578) is given by (36)



1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1198671(120578 119862119894) = 1198621+ 1198622120578 + 11986231205782+ 11986241205783+ 11986251205784

+ (1198626+ 1198627120578 + 11986281205782+ 11986291205783) 119890minus119870120578

(42)


119865 (120578) = 119865 (120578)

+ 1198629[ minus

68041198702+ 793 + 908120573

6481198706

+ (minus1

411987021205784+1215119870

2+ 3872 + 2365120573

2161198706119890minus119870120578

+1198702minus 7 minus 2120573

411987031205783+61198702minus 27 minus 12120573

411987041205782

+331198702minus 123 minus 66120573

81198705120578

+391198702minus 132 minus 78120573

81198706) 119890minus2119870120578

+ (120573 minus 1

1811987031205783+7120573 minus 7

3611987041205782+11120573 minus 11

361198705120578

+131120573 minus 131

6481198706) 119890minus3119870120578

]

(43)

where 119865(120578) is given by (39)



119894which




119877 (120578 119862119894) = 119865101584010158401015840

(120578 119862119894) + 119865 (120578 119862

119894) 11986510158401015840

(120578 119862119894)

+ 120573 (1 minus 11986510158402

(120578 119862119894))

(44)


119894 119894 = 1 2 The


119869119894(119862119895) = int

infin

0

119877 (120578 119862119895) 119891119894(120578) 119889120578 = 0

119894 = 1 2 119902 119895 = 1 2 119902

(45)





1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205785119890minus119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

(46)



(119902 = 11)

1198911= 119890minus119870120578

1198912= 120578119890minus119870120578

1198913= 1205782119890minus119870120578

1198914= 1205783119890minus119870120578

1198915= 1205784119890minus119870120578

1198916= 1205784119890minus2119870120578

+ 120572120578119890minus4119870120578

1198917= 120578119890minus2119870120578

1198918= 1205782119890minus2119870120578

1198919= 1205783119890minus2119870120578

11989110= 1205785119890minus119870120578

+ 120578119890minus3119870120578

11989111= 1205783119890minus4119870120578

+ 1205787119890minus2119870120578

(47)









1198621= minus00974633576 119862

2= 03334342895

1198623= minus00846971328 119862

4= 00054445300

1198625= 108640621331 119862

6= minus89072774043

1198627= 07917175772 119862

8= 04377125759

119870 = 09345058664

(48)







45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 02543480764 02543149422 0000033134185 08550267840 08550621314 00000353473125 16045273996 16043588322 00001685673165 23963133788 23962404320 000007294674 31955002598 31953781616 00001220981245 39954529746 39949610905 00004918840285 47954513976 47946972370 00007541605325 55954513676 55946526226 00007987450365 63954513670 63946242000 000082716708 71954513667 719442747097 00010238957


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05833149514 0000010133785 08760975697 08759651454 00001324243125 09760687561 09759519582 00001167979165 09971920750 09973768978 000018482284 09998081986 09994693079 00003388907245 09999925769 09995222975 00004702794285 09999998398 09998331589 00001666808325 09999999978 10000050268 5028974 sdot 10

minus6

365 09999999995 09998832648 000011673468 09999999995 09996174949 00003825046


119865 (120578)

= minus08095502989 + 120578

+ (minus22237146927 + 02852293525120578

+ 007853895551205782+ 00216006979120578

3

+001155055131205784+ 00011652211120578

5) 119890minus09345058664120578

+ (30954492754 + 20345244657120578

+089052862901205782minus 01261379297120578

3) 119890minus18690117328120578

+ (minus00565973734 + 02080470361120578

minus002694769911205782) 119890minus28035175992120578

minus 00055869102 sdot 119890minus37380234657120578

(49)






1198621= 153365053132 119862

2= minus207743165892

1198623= 93076203696 119862

4= minus20941285422

1198625= 02277189607 119862

6= minus52584096507

1198627= minus455148999446 119862

8= 83240015527

119870 = 21171968259

(50)


119865 (120578) = minus08071635483 + 120578

+ (28068611339 minus 34953295790120578

+ 443038125971205782minus 25930631506120578

3

+ 083303635341205784minus 01666768365120578

5

+001792613681205786) 119890minus21171968259120578







45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 02543480764 02543333746 0000014701785 08550267840 08549561291 00000706549125 16045273996 16042714779 00002559216165 23963133788 23958902142 000042316454 31955002598 31948843675 00006158922245 39954529746 39943062991 00011466754285 47954513976 47936944532 00017569444325 55954513676 55932562778 00021950898365 63954513670 63930163452 000243502188 71954513667 71929060945 00025452721


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048177 05831981849 0000106632785 08760975697 08760769428 00000206268125 09760687561 09757219753 00003467808165 09971920750 09970876920 000010438294 09998081986 09993456222 00004625764245 09999925769 09992025737 00007900032285 09999998398 09993191919 00006806479325 09999999978 09995868200 00004131778365 09999999995 09997970596 000020293988 09999999995 09999136481 00000863514

+ ( minus 20785335331 + 00310432086120578

+ 021756755161205782minus 04253321356120578

3

minus000299933861205784) 119890minus42343936518120578

+ (00788359475 + 01063683100120578

minus002436385171205782) 119890minus63515904777120578

(51)




1198621= 171086190380 119862

2= minus61886479153

1198623= 07626899878 119862

4= minus00317286051

1198625= minus638867694459 119862

6= 07750251041

1198627= minus74945476964 119862

8= minus98195426109

1198629= minus04164447206 119870 = 11269038309

120572 = 08746910670

(52)


119865 (120578) = minus24537934149 + 120578

+ (minus189229176282 + 10563974022120578

+ 366217956051205782minus 10933800148120578

3

+ 012716271841205784

+000563111141205785) 119890minus11269038309120578

+ (199100776837 + 258158411889120578

+931374517661205782+ 19358858129120578

3)

times 119890minus225380766196120578

+ (13951574877 + 07157493617120578

+014547298861205782) 119890minus33807114929120578

+ 00714758716119890minus45076153239120578

(53)








45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 02543480764 02543410815 6994904 sdot 10minus6

85 08550267840 08550382932 00000115092125 16045273993 16045272608 1384603 sdot 10

minus7

165 23963133781 23963351657 000002178764 31955002585 31955812100 00000809514245 39954529727 39955457399 00000927671285 47954513949 47955738251 00001224302325 55954513640 55956241393 00001727753365 63954513623 63956765240 000022516178 71954513606 71957387803 00002874196



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus20

45 05833048175 05832372756 0000067541985 08760975695 08761763161 00000787466125 09760687557 09760153463 00000534094165 09971920744 09972855939 000009351944 09998081978 09998421267 00000339289245 09999925759 10000087749 00000161989285 09999998387 10000557917 00000559529325 09999999965 10000650747 00000650781365 09999999980 10000682953 000006829738 09999999978 10000901947 00000901968



1




1198621= 288801485140 119862

2= minus307469629234

1198623= 101656115824 119862

4= minus13058736876

1198625= 00629713196 119862

6= minus112295919004

1198627= 623525565579 119862

8= minus186274524032

1198629= 137997786872 119870 = 19932224781

(54)

120572 = 27977542979


119865 (120578) = minus08042841228 + 120578

+ (5055972832 minus 74607384673120578

+ 769887395491205782minus 39526112515120578

3

+ 100020019241205784minus 01204170249120578

5

+000526545331205786) 119890minus19932224781120578

+ (minus4126293156 minus 02733114331120578

minus 01516093441205782minus 05576699112120578

3

minus086935553371205784) 119890minus39864449562120578

+ (minus00807202735 minus 02092400883120578

minus001965846811205782minus 00484063456120578

3)

times 119890minus59796674343120578

(55)







45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 02543480764 02543611093 0000013032885 08550267840 08550475945 00000208105125 16045273993 16045751046 00000477053165 23963133781 23963685295 000005515144 31955002585 31955790615 00000788029245 39954529727 39955715667 00001185939285 47954513949 47956217908 00001703959325 55954513640 55956679550 00002165910365 63954513623 63956963294 000024496718 71954513606 71957094147 000025805400



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|

0 1852884 sdot 10minus21



45 05833048175 05833475838 00000427662

85 08760975695 08761071968 9627358 sdot 10minus6

125 09760687557 09760898679 00000211121165 099719207446 09972074735 000001539904 09998081978 09998485848 00000403869245 099999257599 10000520335 00000594575285 099999983873 10000653592 00000655205325 099999999655 10000472907 00000472941365 099999999803 10000244710 000002447308 09999999978 10000098270 9829220 sdot 10

minus6



OHAM(0) 092767733 092763760 092760923 092779335 092768004



1 It





1198621= 59913279914 119862

2= minus66828413743

1198623= 20729320860 119862

4= minus01950415110

1198625= 180871429890 119862

6= minus844868066767

1198627= 176775180449 119862

8= minus03871636300

119870 = 20064973399

(56)




0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0 2229510 sdot 10minus25



45 03124230332 03124218993 1133942 sdot 10minus6

85 09797795327 09797813157 1783054 sdot 10minus6

125 17552539494 17552573134 3364056 sdot 10minus6

165 25523254690 25523466484 000002117944 33521093590 33521308223 000002146329245 41520998358 41521444024 00000445665285 49520995946 49522018532 00001022586325 57520995955 57522601900 00001605945365 65520996012 65522991212 000019951998 73520996086 73523194836 00002198750


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859347711 2696657 sdot 10minus6

85 09323482529 09323468816 1371273 sdot 10minus6

125 09905493983 09905683352 000001893165 09991860373 09991967641 0000010724 09999584304 09999621135 3683007 sdot 10

minus6

245 09999987792 10000547905 00000560112285 09999999836 10000795225 00000795389325 10000000061 10000621951 00000621890365 10000000081 10000356813 000003567318 10000000101 10000168920 00000168818


119865 (120578) = minus06476658539 + 120578

+ (11858804994 minus 10205705493120578

+ 119122236381205782minus 07433934009120578

3

+ 019803635041205784minus 00194409937120578

5)

times 119890minus20064973399120578

+ (minus05332638964 + 02249079388120578

+ 030838213061205782+ 00240412688120578

3)

times 119890minus40129946798120578

+ (minus0004950749 + 00053425041120578) 119890minus60194920197120578

(57)



1198621= 256413506662 119862

2= minus277257520445

1198623= 102440262047 119862

4= minus16311566772

1198625= 01133872279 119862

6= minus378620215531

1198627= 45810479839 119862

8= minus97143709526

119870 = 20340821793

(58)


119865 (120578) = minus06482098275 + 120578

+ (17192094539 minus 45907375859120578

+ 533338769141205782minus 30101935973120578

3

+ 089735163491205784minus 01394863598120578

5

+ 000929061341205786) 119890minus20340821793120578




0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0 2229510 sdot 10minus25



45 03124230332 03124250905 20573489 sdot 10minus6

85 09797795327 09797816632 21304868 sdot 10minus6

125 17552539494 17552458857 8063655 sdot 10minus6

165 25523254690 25523068656 000001860334 33521093590 33520844463 00000249127245 41520998358 41520336380 00000661977285 49520995946 49519649131 00001346814325 57520995955 57518965404 00002030550365 65520996012 65518462101 000025339118 73520996086 73518163433 00002832652


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|




45 06859374677 06859334525 4015197 sdot 10minus6

85 09323482529 09323592586 00000110057125 09905493983 09905212799 00000281183165 09991860373 09991867807 7433778 sdot 10

minus7

4 09999584304 09999317943 00000266361245 09999987792 09999248393 00000739398285 09999999836 09999090229 00000909606325 10000000061 09999238617 00000761443365 10000000081 09999506141 000004939408 10000000101 09999733687 00000266414

+ (minus10709996263 + 27307483905120578

+ 235999247461205782+ 05869724289120578

3)

times 119890minus40681643586120578

(59)




1198621= 151069993472 119862

2= minus61116892850

1198623= 08419581636 119862

4= minus00391594463

1198625= minus3481410130441 119862

6= 3546124244346

1198627= minus782878044901 119862

8= minus38910409852

1198629= minus43179402181 119870 = 13940527605

120572 = 12080121437

(60)


119865 (120578) = minus06477776791 + 120578

+ (minus18001344737 + 22989361198120578

+ 241303281271205782minus 08773035418120578

3

+ 011544312741205784minus 00056180723120578

5)

times 119890minus13940527605120578

+ (18631306321 + 23515563981120578

+ 123576021611205782+ 33122912941120578

3

+055546693571205784) 119890minus27881055211120578

+ (00178160913 + 01112333145120578) 119890minus41821582817120578

(61)





0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0 4693280 sdot 10minus25



45 03124230332 03124256050 25717950 sdot 10minus6

85 09797795326 09797870784 7545842 sdot 10minus6

125 17552539491 17552584440 4494942 sdot 10minus6

165 25523254682 25523369280 000001145974 33521093576 33521193533 9995766 sdot 10

minus6

245 41520998332 41521125574 00000127241285 49520995903 49521192859 00000196955325 57520995889 57521233093 00000237203365 65520995917 65521296538 000003006208 73520995953 73521431339 00000435385



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 06859374676 06859366849 7826990 sdot 10minus7

85 09323482527 09323490349 7821535 sdot 10minus7

125 09905493979 09905533068 3908903 sdot 10minus6

165 09991860366 09991905903 4553709 sdot 10minus6

4 09999584293 09999557316 2697690 sdot 10minus6

245 09999987775 10000074611 8683616 sdot 10minus6

285 09999999812 10000067856 6804426 sdot 10minus6

325 10000000029 10000048084 4805536 sdot 10minus6

365 10000000039 10000121725 000001216858 10000000049 10000209604 00000209554



1198621= 25755597425 119862

2= minus05965183787

1198623= minus00172692621 119862

4= 00136562951

1198625= minus00010079176 119862

6= minus59530458601

1198627= minus19930045747 119862

8= minus19931630292

1198629= 00743455822 119870 = 11143724942

120572 = 02855970092

(62)


119865 (120578) = minus06475361092 + 120578

+ (minus70772773941 + 15599095672120578

+ 038334817081205782minus 0141867195120578

3

+ 000688201361205784+ 00015709234120578

5

minus 000015074511205786) 119890minus11143724942120578

+ (77248135031 + 67700065534120578

+ 226850164451205782+ 02970574871120578

3

minus 00149669871205784) 119890minus22287449884120578

(63)









0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












0 4693280 sdot 10minus25 0 4693280 sdot 10

minus25

45 03124230332 03124174580 5575244 sdot 10minus6

85 09797795326 09797740164 5516204 sdot 10minus6

125 17552539491 17552534223 5267840 sdot 10minus7

165 25523254682 25523611425 000003567424 33521093576 33521105770 1219470 sdot 10

minus6

245 41520998332 41521005519 7187418 sdot 10minus7

285 49520995903 49521462123 00000466219325 57520995889 57521684524 00000688634365 65520995917 65521510110 000005141928 73520995953 73521263893 00000267940



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|


minus21

45 06859374676 06859539897 0000016522085 09323482527 09323092256 00000390271125 09905493979 09906138617 00000644637165 09991860366 09991779292 8107355 sdot 10

minus6

4 09999584293 09999145872 00000438420245 09999987775 10000414108 00000426333285 09999999812 10000539936 00000540124325 10000000029 09999989176 1085287 sdot 10

minus6

365 10000000039 09999655183 000003448568 10000000049 09999795865 00000204184



OHAM(0) 123258247 123257895 123262084 123257391 1232558769



2= 26648959478

1198623= minus05277449747 119862

4= 00344313836

1198625= 09084258281 119862

6= 111816458907

1198627= minus05492649796 119862

8= 15695573134

119870 = 17389825314

(64)


119865 (120578) = minus05440478033 + 120578

+ (16577374986 minus 04175138596120578

minus 047229334011205782+ 02774993818120578

3

minus 0055443815881205784+ 00039599458120578

5)

times 119890minus17389825314120578

+ (minus11629370587 minus 15183251610120578

minus 075786653251205782minus 01287736808120578

3)

times 119890minus34779650629120578

+ (00455165672 + 00373698159120578

minus 000348156891205782) 119890minus52169475944120578

+ 00037307962119890minus69559301258120578

(65)



1198621= 121397319477 119862

2= minus147300094090

1198623= 60298078722 119862

4= minus10787489057







45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 03599784956 03599782796 2160525 sdot 10minus7

85 10696147641 10696156734 9093019 sdot 10minus7

125 18571623264 18571633242 9977941 sdot 10minus7

165 26560434964 26560463745 2878145 sdot 10minus6

4 34559804211 34559769848 3436309 sdot 10minus6

245 42559782714 42559782610 1038556 sdot 10minus8

285 50559782427 50559829283 4685640 sdot 10minus6

325 58559782660 58559798484 1582358 sdot 10minus6

365 66559783023 66559717863 6516027 sdot 10minus6

8 74559783545 74559638500 00000145044


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609240247 1486624 sdot 10minus6

85 09619780339 09619706813 7352687 sdot 10minus6

125 09960567187 09960657372 9018419 sdot 10minus6

165 09997439284 09997365151 7413383 sdot 10minus6

4 09999899725 09999872482 2724280 sdot 10minus6

245 09999997837 10000081444 8360731 sdot 10minus6

285 10000000206 10000013591 1338446 sdot 10minus6

325 10000000368 09999918129 8223935 sdot 10minus6

365 10000000541 09999891905 000001086358 10000000764 09999914106 8665844 sdot 10

minus6

1198625= 00852147302 119862

6= minus148695758423

1198627= minus78344847253 119862

8= minus24044068709

119870 = 20881719331

(66)


119865 (120578) = minus0544241252 + 120578

+ (0398631080 minus 1040810138120578

+ 1699497611205782minus 1248940652120578

3

+ 04606770861205784minus 0086297165120578

5

+ 0006801381205786) 119890minus2088171933120578

+ (0219770025 + 1364996288120578

+ 10255460391205782+ 0114703592120578

3

+ 00014038061205784) 119890minus4176343866120578

+ (minus00741598535 minus 0038516290120578

minus 00088021331205782) 119890minus6264515799120578

(67)




1198621= 37343092835 119862

2= minus16919201004

1198623= 02585003215 119862

4= minus00131947678

1198625= 269486507241 119862

6= minus475028568351

1198627= 53389432018 119862

8= minus87586264382

1198629= 02924008927 119870 = 14882721635

120572 = 19742364175690

(68)







45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 03599784956 03599798414 1345740 sdot 10minus6

85 10696147641 10696168199 2055868 sdot 10minus6

125 18571623264 18571595718 2754588 sdot 10minus6

165 26560434964 26560360629 7433444 sdot 10minus6

4 34559804211 34559769853 3435805 sdot 10minus6

245 42559782714 42559486488 00000296226285 50559782427 50558929543 00000852884325 58559782660 58558366505 00001416154365 66559783023 66557973327 000018096968 74559783545 74557756153 00002027391


120578 1198651015840

numerical(120578) 1198651015840


OHAM(120578)|

0 4071713 sdot 10minus20



45 07609225381 07609190201 3517984 sdot 10minus6

85 09619780339 09619872725 9238582 sdot 10minus6

125 09960567187 09960397833 00000169354165 09997439284 09997513373 7408827 sdot 10

minus6

4 09999899725 09999817723 8200210 sdot 10minus6

245 09999997837 09999433979 00000563857285 10000000206 09999242317 00000757889325 10000000368 09999386977 00000613391365 10000000541 09999628614 000003719268 10000000764 09999814328 00000186436


119865 (120578) = minus0544001931 + 120578

+ (minus4354906951 + 13261535367120578

+ 030724494731205782+ 01940259496120578

3

+ 003153090321205784minus 00017731659120578

5)

times 119890minus14882721635120578

+ (48182102767 + 60137273891120578

+ 244512568211205782+ 08109067414120578

3

minus 003300304331205784) 119890minus2976544327120578

+ (01139109044 minus 0168675728120578

+ 00609401041205782+ 00029567211120578

3)

times 119890minus44648164905120578

minus 0033212299119890minus59530886541120578






2= 68914081433

1198623= minus17496966452 119862

4= 02003197512

1198625= minus00103677381 119862

6= 101134115449

1198627= 70897290367 119862

8= 19899138244

1198629= 00159776712 119870 = 15329158534

120572 = minus09799303286

(70)







45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 03599784956 03599790235 5278046 sdot 10minus7

85 10696147640 10696154385 6744980 sdot 10minus7

125 18571623261 18571642418 1915749 sdot 10minus6

165 26560434955 26560445435 1048024 sdot 10minus6

4 34559804190 34559816246 1205614 sdot 10minus6

245 42559782671 42559820737 3806680 sdot 10minus6

285 50559782344 50559813610 3126620 sdot 10minus6

325 58559782515 58559788900 6385224 sdot 10minus7

365 66559782783 66559788961 6177966 sdot 10minus7

8 74559783175 74559820586 374109314 sdot 10minus6



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232141 6760967 sdot 10minus7

85 09619780338 09619796540 1620229 sdot 10minus6

125 09960567183 09960575197 8014067 sdot 10minus7

165 09997439274 09997418375 2089891 sdot 10minus6

4 09999899704 09999929170 2946522 sdot 10minus6

245 09999997799 10000016372 1857256 sdot 10minus6

285 10000000145 09999969829 3031551 sdot 10minus6

325 10000000272 09999978766 2150573 sdot 10minus6

365 10000000399 10000022282 2188252 sdot 10minus6

8 10000000667 10000052427 5176061 sdot 10minus6


119865 (120578) = minus05439219913 + 120578

+ (4650996506 minus 20398248866120578

minus 048584461351205782+ 0550362856120578

3

minus 016036168771205784+ 00213068753120578

5

minus 000112723491205786) 119890minus15329158534120578

+ (minus42651113968 minus 42739140037120578

minus 16609923091205782minus 02098183934120578

3

minus 000213161251205784) 119890minus30658317069120578

+ (0158036881 + 00939831378120578

+ 001875200871205782+ 00001478554120578

3)

times119890minus45987475603120578

(71)

1 2 3 4

05

10

15

20

25

30

35

F

120578

120573 = 12 1 16









45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















45 035997849 03599784037 9195208 sdot 10minus8

85 106961476 10696144385 3254580 sdot 10minus7

125 185716232 18571634346 1108560 sdot 10minus6

165 265604349 26560430260 4694645 sdot 10minus7

4 3455980419 34559810382 6192629 sdot 10minus7

245 425597826 42559845299 6262826 sdot 10minus6

285 505597823 50559832266 4992205 sdot 10minus6

325 585597825 58559812915 3039980 sdot 10minus6

365 665597827 66559890626 000001078428 74559783175 74560065554 00000282378



120578 1198651015840

numerical(120578) 119865

1015840


OHAM(120578)|




45 07609225380 07609232919 7538631 sdot 10minus7

85 09619780338 09619761488 1885029 sdot 10minus6

125 09960567183 09960594353 2717000 sdot 10minus6

165 09997439274 09997398342 4093197 sdot 10minus6

4 09999899704 09999971751 7204662 sdot 10minus6

245 09999997799 10000032843 3504355 sdot 10minus6

285 10000000145 09999951986 4815848 sdot 10minus6

325 10000000272 10000024525 2425327 sdot 10minus6

365 10000000399 10000168296 000001678968 10000000667 10000253832 00000253165




119865

10158401015840

OHAM(0) 152151589 152151820 152151245 152151403 152151402

1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16




1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16



1given by (34) (37) (40) and (42) are



1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16




1


6 Conclusions


1 2 3 4

10

08

06

04

02

120578

F998400

120573 = 12 1 16


1 2 3 4

05

10

15

20

25

30

35

120578

F

120573 = 12 1 16


1 2 3 4

10

08

06

04

02

120578

F998400 120573 = 12 1 16









119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















119894











1lead




References





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Documents

Research Article Analytic Approximate Solution for Falkner-Skan …downloads.hindawi.com/journals/tswj/2014/617453.pdf · 2019-07-31 · Research Article Analytic Approximate Solution