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PlotTableSum2(-1)n+1
nSin[n θ], {n, 1, k}, {k, 1, 5}, θ, {θ, -π, π}
-3 -2 -1 1 2 3
-3
-2
-1
1
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PlotTableSum2(-1)n+1
nSin[n θ], {n, 1, k}, {k, 1, 5}, θ, {θ, -2 π, 2 π}
-6 -4 -2 2 4 6
-6
-4
-2
2
4
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PlotTableSum2(-1)n+1
nSin[n θ], {n, 1, k}, {k, 10, 15}, θ, {θ, -2 π, 2 π}
-6 -4 -2 2 4 6
-6
-4
-2
2
4
6
PlotTableSum2(-1)n+1
nSin[n θ], {n, 1, k}, {k, 30, 35}, θ, {θ, -π, π}
-3 -2 -1 1 2 3
-3
-2
-1
1
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PlotTableSum2(-1)n+1
nSin[n θ], {n, 1, k}, {k, 1, 35}, θ, {θ, -π, π}
-3 -2 -1 1 2 3
-3
-2
-1
1
2
3
f = 1 - (t/π)2
1 -t2
π2
FourierCoefficient[f, t, n]
BesselJ[1, n π]
2 n
ListPlotTableLogAbsBesselJ[1, Exp[n] π]
2 Exp[n], {n, 1, 100}
20 40 60 80 100
-140
-120
-100
-80
-60
-40
-20
Plot[Evaluate[{Table[FourierSeries[f, t, n], {n, 5, 9}], f}], {t, -π, π}]
-3 -2 -1 1 2 3
0.2
0.4
0.6
0.8
1.0
Plot[Evaluate[Table[FourierSeries[f, t, n], {n, 5, 9}]], {t, -2 π, 2 π}, AspectRatio → 1/4]
-6 -4 -2 2 4 6
0.4
0.6
0.8
1.0
Plot[Evaluate[Table[FourierSeries[f, t, n], {n, 10, 15}]], {t, -2 π, 2 π}, AspectRatio → 1/3]
-6 -4 -2 2 4 6
0.4
0.6
0.8
1.0
Plot[Evaluate[{Table[FourierSeries[f, t, n], {n, 10, 15}], f}], {t, -π, π}, AspectRatio → 1/2]
-3 -2 -1 1 2 3
0.2
0.4
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0.8
1.0
g = (1 - t/π)/2
1
21 -
t
π
FourierSinCoefficient[g, t, n]
1
n π
gg = If[t < 0, (-1 - t/π)/2, (1 - t/π)/2]
Ift < 0,1
2-1 -
t
π,
1
21 -
t
π
Plot[gg, {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
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F[t_, n_] := FourierSinSeries[g, t, n]
sigma[t_, n_] :=1
n
i=1
n
FourierSinSeries[g, t , i]
Plot[Evaluate[Table[F[t, n], {n, 10, 15}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
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Plot[Evaluate[Table[F[t, n], {n, 25, 30}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
0.2
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Plot[Evaluate[Table[sigma[t, n], {n, 10, 15}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
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Plot[Evaluate[Table[sigma[t, n], {n, 15, 30}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
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Plot[Evaluate[{gg, F[t, 30], sigma[t, 30]}], {t, -π, π}, PlotStyle → {Thick, Thick, Thick}]
-3 -2 -1 1 2 3
-0.4
-0.2
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Di[n_] :=1
2 π
Sin[(n + 1/2) x]
Sin[x/2]
Plot[Di[10], {x, 0, 2 π}, PlotRange → All]
1 2 3 4 5 6
1
2
3
Plot[Di[20], {x, 0, 2 π}, PlotRange → All]
1 2 3 4 5 6
2
4
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Plotx Di[10], x1
2 π Sin[x/2], {x, 0, π}, PlotRange → All
0.5 1.0 1.5 2.0 2.5 3.0
-0.4
-0.2
0.2
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