File:Stirling series relative error.svg
Original file (SVG file, nominally 740 × 530 pixels, file size: 109 KB)
Captions
This file supersedes the file StirlingErrorGraphBB.svg. It is recommended to use this file rather than the other one.
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Summary edit
DescriptionStirling series relative error.svg |
English: Plot of the relative error in the Stirling series as compared with the gamma function. Recursion relation for the an coefficients taken from Mathworld |
Date | |
Source | Own work |
Author | Glosser.ca |
SVG development InfoField | This diagram was created with Mathematica. |
Source code InfoField | Mathematica codeb[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_] := Exp[-z] z^(z - 1/2) Sqrt[2 \[Pi]] Sum[a[k] z^-k, {k, 0, n}]
LogLinearPlot[
Evaluate@Table[Log[10, Abs[(Approx[x, n] - Gamma[x])/Gamma[x]]], {n, 0, 5}],{x, 1, 10^9},
PlotRange -> All,
WorkingPrecision -> 120,
Frame -> True,
FrameTicks -> {Table[{10^k, Superscript[10, k]}, {k, 0, 9}], Automatic},
FrameLabel -> {"Argument", Log["Relative Error"]},
PlotLegends -> LineLegend[Range[0, 5], LegendLabel -> "Number of terms"],
ImageSize -> Large,
PlotStyle -> Thick,
FrameStyle -> Directive[Black],
GridLines -> {10^Range[0, 9], Automatic},
GridLinesStyle -> Directive[LightGray, Dashed]
]
|
Licensing edit
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- to share – to copy, distribute and transmit the work
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- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:02, 23 April 2016 | 740 × 530 (109 KB) | Rayhem (talk | contribs) | Add 10px margin | |
18:01, 23 April 2016 | 715 × 505 (109 KB) | Rayhem (talk | contribs) | Move legend to top of plot | ||
21:42, 22 April 2016 | 859 × 481 (83 KB) | Rayhem (talk | contribs) | User created page with UploadWizard |
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Width | 592.29688pt |
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Height | 424.39386pt |