File:LogConvergenceAnim.gif
Summary
| Description |
English: A plot showing the convergence of the power series about 1 for log at .
Category:PNG created with Mathematica#LogConvergenceAnim.gif |
| Date | |
| Source | Own work |
| Author | Kan8eDie |
Source
Export["anim.gif",
Table[
ListPlot[
Table[
it =
Normal[Series[Log[z + 1] , {z, 0, n}]] /.
z -> Exp[(\[Pi] - 1/3) I];
{Re[it], Im[it]},
{n, 0, a}
],
PlotRange -> {0, 1.8},
Joined -> True,
Mesh -> All,
AxesLabel -> {Style[\[GothicCapitalR], Medium],
Style[\[GothicCapitalI], Medium]},
AspectRatio -> 1,
ImageSize -> 500,
Epilog -> {it = Log[1 + Exp[(\[Pi] - 1/3) I]];
Darker[Blue], Text[
Style[
HoldForm[
Subscript[z, n] =
Sum[(-1)^(k + 1) \[ExponentialE]^(k i (\[Pi] - 1/3))/k, {k,
1, n}]], 15, Antialiasing -> True
], {-0.8, 0.5}
],
Red,
PointSize[0.01], Point[{Re[it], Im[it]}],
Text[Style[
HoldForm[
Log[1 + \[ExponentialE]^(i (\[Pi] - 1/3))] =
Sum[(-1)^(k + 1) \[ExponentialE]^(k i (\[Pi] - 1/3))/k, {k,
1, Infinity}]], 15
], {Re[it], Im[it] - 0.2}, {-0.6, 1}]
}
], {a, 5, 77, 3}],
"DisplayDurations" -> PadLeft[{1}, 25, 0.1]
]
Licensing
 |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
