PlotTableSum2
(-1)n+1
Sin[n θ], {n, 1, k}, {k, 1, 5}, θ, {θ, -π, π}
n
3
2
1
-3
-2
1
-1
2
3
-1
-2
-3
PlotTableSum2
(-1)n+1
Sin[n θ], {n, 1, k}, {k, 1, 5}, θ, {θ, -2 π, 2 π}
n
6
4
2
-6
-4
2
-2
4
6
-2
-4
-6
PlotTableSum2
(-1)n+1
Sin[n θ], {n, 1, k}, {k, 10, 15}, θ, {θ, -2 π, 2 π}
n
6
4
2
-6
-4
2
-2
4
6
-2
-4
-6
PlotTableSum2
(-1)n+1
Sin[n θ], {n, 1, k}, {k, 30, 35}, θ, {θ, -π, π}
n
3
2
1
-3
-2
1
-1
2
3
-1
-2
-3
PlotTableSum2
(-1)n+1
Sin[n θ], {n, 1, k}, {k, 1, 35}, θ, {θ, -π, π}
n
3
2
1
-3
-2
1
-1
2
3
-1
-2
-3
1 - (t / π)2
f =
t2
1- 2
π
FourierCoefficient[f, t, n]
BesselJ[1, n π]
2n
ListPlotTableLogAbs
20
BesselJ[1, Exp[n] π]
, {n, 1, 100}
2 Exp[n]
40
60
80
100
-20
-40
-60
-80
-100
-120
-140
Plot[Evaluate[{Table[FourierSeries[f, t, n], {n, 5, 9}], f}], {t, -π, π}]
1.0
0.8
0.6
0.4
0.2
-3
-2
1
-1
2
3
Plot[Evaluate[Table[FourierSeries[f, t, n], {n, 5, 9}]], {t, -2 π, 2 π}, AspectRatio → 1 / 4]
1.0
0.8
0.6
0.4
-6
-4
2
-2
4
6
Plot[Evaluate[Table[FourierSeries[f, t, n], {n, 10, 15}]], {t, -2 π, 2 π}, AspectRatio → 1 / 3]
1.0
0.8
0.6
0.4
-6
-4
2
-2
4
6
Plot[Evaluate[{Table[FourierSeries[f, t, n], {n, 10, 15}], f}], {t, -π, π}, AspectRatio → 1 / 2]
1.0
0.8
0.6
0.4
0.2
-3
-2
1
-1
2
3
g = (1 - t / π) / 2
1
t
1 - 
2
π
FourierSinCoefficient[g, t, n]
1
nπ
gg = If[t < 0, (-1 - t / π) / 2, (1 - t / π) / 2]
Ift < 0,
1
t
1
t
-1 - ,
1 - 
2
π
2
π
Plot[gg, {t, -π, π}]
0.4
0.2
-3
-2
1
-1
2
3
-0.2
-0.4
F[t_, n_] := FourierSinSeries[g, t, n]
sigma[t_, n_] :=
1 n
 FourierSinSeries[g, t , i]
n i=1
Plot[Evaluate[Table[F[t, n], {n, 10, 15}]], {t, -π, π}]
0.4
0.2
-3
-2
-1
1
2
3
1
2
3
-0.2
-0.4
Plot[Evaluate[Table[F[t, n], {n, 25, 30}]], {t, -π, π}]
0.4
0.2
-3
-2
-1
-0.2
-0.4
Plot[Evaluate[Table[sigma[t, n], {n, 10, 15}]], {t, -π, π}]
0.4
0.2
-3
-2
1
-1
2
3
-0.2
-0.4
Plot[Evaluate[Table[sigma[t, n], {n, 15, 30}]], {t, -π, π}]
0.4
0.2
-3
-2
1
-1
2
3
-0.2
-0.4
Plot[Evaluate[{gg, F[t, 30], sigma[t, 30]}], {t, -π, π}, PlotStyle → {Thick, Thick, Thick}]
0.4
0.2
-3
-2
1
-1
2
3
-0.2
-0.4
Di[n_] :=
1 Sin[(n + 1 / 2) x]
2π
Sin[x / 2]
Plot[Di[10], {x, 0, 2 π}, PlotRange → All]
3
2
1
1
2
3
2
3
4
5
6
Plot[Di[20], {x, 0, 2 π}, PlotRange → All]
6
4
2
1
Plotx Di[10], x
4
5
1
, {x, 0, π}, PlotRange → All
2 π Sin[x / 2]
0.4
0.2
-0.2
-0.4
0.5
1.0
1.5
2.0
2.5
3.0
6