Functional Expansions II

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  • 8/9/2019 Functional Expansions II

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    2014

    :

    .

    :

    :=

    = 1 2

    1

    ( ) ( )n

    k n

    k

    t z t t t z RRRR , =

    =1

    ( ) lim ( )n

    kn

    k

    T z t z RRRR .

    :

    =

    = 1 1

    1

    ( ) ( )n

    k n n

    k

    t z t t t z LLLL , =

    =1

    ( ) lim ( )n

    kn

    k

    T z t z LLLL .

    1. ,

    . .

    (1)

    = + + + , < ( )

    :

    (2)

    = +

    1

    (3)

    +=

    = +

    RRRR

    =

    ,

    C :

    (4)

    += + , =

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    1 (, 2011) ( ) = + , 1z R

    < < . 10

    r R< < , ( )

    1

    1

    ( )1

    k

    k

    R rR R r

    =

    = = + .

    = z R

    ( )

    =

    + < , 1k kR

    r =

    =

    +

    , , = ( ).

    : = +

    +=

    = +

    RRRR , 20

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    : = +

    +=

    = +

    RRRR , 40

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    2(, 2011) n{g } S=(|z| . , ( )0 0z S z R = < ,

    n n n 1 1G (z) g g g (z) G(z)= , 0S .

    :

    = + + ,

    = 20

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    (9) = + = + + ,

    (10)

    +=

    = +

    RRRR

    : = +

    +=

    = +

    RRRR 40

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    :

    +=

    = + = +

    RRRR , 45

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    : = +

    ( )

    +=

    = +

    RRRR 40

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    :( )

    +=

    = + = +

    RRRR 40

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