File:AsymptoticExpansionExample.svg
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Size of this PNG preview of this SVG file: 449 × 273 pixels. Other resolutions: 320 × 195 pixels | 640 × 389 pixels | 1,024 × 623 pixels | 1,280 × 778 pixels | 2,560 × 1,557 pixels.
Original file (SVG file, nominally 449 × 273 pixels, file size: 68 KB)
Summary
| Description |
English: Plots of the absolute value of the fractional error in the asymptotic expansion of the Gamma-related function . The horizontal axis is the number of terms in the asymptotic expansion. Blue points are for x=2 and red points are for x=3. It can be seen that the least error is encountered when there are 14 terms for x=2, and 20 terms for x=3, beyond which the error diverges. |
| Date | |
| Source | Own work |
| Author | PAR |
| SVG development |  This plot was created with Mathematica. |
| Source code | Mathematica codef[x_] := Exp[x] Gamma[x + 1]/x^x/Sqrt[2 \[Pi] x]
ff[n_, x_] := Normal[Series[f[xx], {xx, \[Infinity], n}]] /. xx -> x
x1 = 2.;
x2 = 3.;
n = 40;
a1 = Table[ff[i, x1], {i, 1, n}];
a2 = Table[ff[i, x2], {i, 1, n}];
plot1 = ListLogPlot[Abs[a1/f[x1] - 1],
PlotRange -> {{0, n + 1}, {10^(-10), 1}}];
plot2 = ListLogPlot[Abs[a2/f[x2] - 1],
PlotRange -> {{0, n + 1}, {10^(-10), 1}}, PlotStyle -> Red];
w = Show[plot1, plot2]
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Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 01:00, 19 January 2017 | | 449 × 273 (68 KB) | wikimediacommons>PAR | absolute value of error rather than error |
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