File:Stirling series relative error.svg
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Size of this PNG preview of this SVG file: 740 × 530 pixels. Other resolutions: 320 × 229 pixels | 640 × 458 pixels | 1,024 × 733 pixels | 1,280 × 917 pixels | 2,560 × 1,834 pixels.
Original file (SVG file, nominally 740 × 530 pixels, file size: 109 KB)
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This file supersedes the file StirlingErrorGraphBB.svg. It is recommended to use this file rather than the other one.
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Summary
| Description |
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 |  This diagram was created with Mathematica. |
| Source code | 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]
]
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- 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.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:02, 23 April 2016 | | 740 × 530 (109 KB) | wikimediacommons>Rayhem | Add 10px margin |
File usage
The following 3 pages use this file:
