t 1 BesselJ 1, n 2 nfig.if.usp.br/~marchett/fismat1/fourier_identidade-semi... · 2016-03-11 ·...
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PlotTableSum2 (- 1) n+1 n Sin[n θ], {n, 1, k}, {k, 1, 5}, θ, {θ, - π, π} -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 PlotTableSum2 (- 1) n+1 n Sin[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 6 PlotTableSum2 (- 1) n+1 n Sin[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 n Sin[n θ], {n, 1, k}, {k, 30, 35}, θ, {θ, - π, π} -3 -2 -1 1 2 3 -3 -2 -1 1 2 3 PlotTableSum2 (- 1) n+1 n Sin[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 - t 2 π 2 FourierCoefficient[f, t, n] BesselJ[1, n π] 2n ListPlotTableLogAbs BesselJ[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 0.6 0.8 1.0 g =(1 - t / π)/ 2 1 2 1 - 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 2 1 - t π Plot[gg, {t, - π, π}] -3 -2 -1 1 2 3 -0.4 -0.2 0.2 0.4 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 0.2 0.4 Plot[Evaluate[Table[F[t, n], {n, 25, 30}]], {t, - π, π}] -3 -2 -1 1 2 3 -0.4 -0.2 0.2 0.4 Plot[Evaluate[Table[sigma[t, n], {n, 10, 15}]], {t, - π, π}] -3 -2 -1 1 2 3 -0.4 -0.2 0.2 0.4 Plot[Evaluate[Table[sigma[t, n], {n, 15, 30}]], {t, - π, π}] -3 -2 -1 1 2 3 -0.4 -0.2 0.2 0.4 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 0.2 0.4 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 6 Plotx Di[10], x 1 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 0.4
Transcript of t 1 BesselJ 1, n 2 nfig.if.usp.br/~marchett/fismat1/fourier_identidade-semi... · 2016-03-11 ·...
![Page 1: t 1 BesselJ 1, n 2 nfig.if.usp.br/~marchett/fismat1/fourier_identidade-semi... · 2016-03-11 · Plot Table Sum 2 (-1)n+1 n Sin[nθ], {n, 1, k} , {k, 1, 5} , θ , {θ, -π,π} -3](https://reader031.fdocuments.pl/reader031/viewer/2022011817/5e77e438e6bf11463629ee22/html5/thumbnails/1.jpg)
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
2
3
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
6
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
2
3
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
0.6
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
0.2
0.4
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
0.2
0.4
Plot[Evaluate[Table[F[t, n], {n, 25, 30}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
0.2
0.4
Plot[Evaluate[Table[sigma[t, n], {n, 10, 15}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
0.2
0.4
Plot[Evaluate[Table[sigma[t, n], {n, 15, 30}]], {t, -π, π}]
-3 -2 -1 1 2 3
-0.4
-0.2
0.2
0.4
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
0.2
0.4
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
6
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
0.4
![arXiv:1508.07560v1 [hep-ex] 30 Aug 2015arXiv:1508.07560v1 [hep-ex] 30 Aug 2015 Study ofDynamics of D0 →K −e+ν e and D0 →π−e+ν e Decays M. Ablikim 1, M. N. Achasov9,f, X.](https://static.fdocuments.pl/doc/165x107/5f6a56e5720e1d4cd57f8d7a/arxiv150807560v1-hep-ex-30-aug-2015-arxiv150807560v1-hep-ex-30-aug-2015.jpg)
