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File:Stirling error vs number of terms.svg

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minor quality

Summary edit

Description
English: Plot of the error in the Stirling series for a fixed argument with increasing numbers of series terms.
Date
Source Own work
Author Glosser.ca
Other versions File:StirlingError.svg Image:StirlingError.png File:StirlingError1.svg
SVG development
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Source code
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Mathematica code

b[0] = b[1] = 1;
b[n_] := b[n] = 
  1/(n + 1) (b[n - 1] - Sum[k b[k] b[n + 1 - k], {k, 2, n - 1}])
a[n_] := (2 n + 1)!! b[2 n + 1]

Approx[z_, n_] := Sqrt[2 \[Pi] z] (z/E)^z Sum[a[k] z^-k, {k, 0, n}]

err[z_, n_] := Abs[(Approx[z, n] - z!)/z!]

Block[{$MaxExtraPrecision = 150},
  ListLogPlot[
   {
    err[10, #] & /@ Range[0, 200],
    err[20, #] & /@ Range[0, 200],
    err[30, #] & /@ Range[0, 200]
    },
   Joined -> True,
   Frame -> True,
   ImageSize -> Large,
   PlotStyle -> Thick,
   FrameStyle -> Directive[Black],
   FrameLabel -> {"Number of terms", "Relative Error"},
   FrameTicks -> {{Automatic, Automatic}, {Range[0, 200, 25], 
      Automatic}},
   GridLines -> {Range[0, 200, 25], Automatic},
   GridLinesStyle -> Directive[LightGray, Dashed],
   PlotLegends -> Placed[
     LineLegend[{10, 20, 30}, LegendLabel -> "Argument, n:"],
     Top
     ]
   ]
  ]

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I, the copyright holder of this work, hereby publish it under the following license:
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current18:04, 23 April 2016Thumbnail for version as of 18:04, 23 April 2016736 × 499 (80 KB)Rayhem (talk | contribs)Fix margins
13:35, 23 April 2016Thumbnail for version as of 13:35, 23 April 2016715 × 501 (80 KB)Rayhem (talk | contribs)User created page with UploadWizard

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