File:LogConvergenceAnim.gif

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LogConvergenceAnim.gif(500 × 516 pixels, file size: 210 KB, MIME type: image/gif, looped, 25 frames, 3.4 s)

Summary[edit]

Description
English: A plot showing the convergence of the power series about 1 for log at .
Icon Mathematical Plot.svg
This mathematical image was created with Mathematica.
Date
Source Own work
Author Kan8eDie

Source[edit]

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[edit]

Public domain 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.

File history

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Date/TimeThumbnailDimensionsUserComment
current09:32, 10 February 2009Thumbnail for version as of 09:32, 10 February 2009500 × 516 (210 KB)Kan8eDie (talk | contribs){{Information |Description={{en|1=A plot showing the convergence of the power series about 1 for log at <math>e^{i (\pi - \frac{1}{3})}</math>. {{Mathematica}}}} |Source=Own work by uploader |Author=Kan8eDie |Date=2008-02-10 |Permission=
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