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File:Mplwp factorial gamma stirling.svg

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Summary

Description
English: Plot of the factorial, gamma function and Stirling's approximation in the interval [−0.2, 3.2]:
Date
Source Own work
Author Geek3
Other versions Mplwp gamma stirling.svg
SVG development
InfoField
 
The source code of this SVG is invalid due to mplwp errors.
 
This W3C-invalid vector image was created with Inkscape, or with something else.
This image has been assessed using the Quality image guidelines and is considered a Quality image.

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Source code
InfoField

mplwp source code

The plot was generated with mplwp 1.6.3
#!/usr/bin/python
# -*- coding: utf8 -*-

import matplotlib.pyplot as plt
import matplotlib as mpl
import numpy as np
from math import *

code_website = 'http://commons.wikimedia.org/wiki/User:Geek3/mplwp'
try:
    import mplwp
except ImportError, er:
    print 'ImportError:', er
    print 'You need to download mplwp.py from', code_website
    exit(1)

name = 'mplwp_factorial_gamma_stirling.svg'
fig = mplwp.fig_standard(mpl)

xlim = -0.2, 3.2; fig.gca().set_xlim(xlim)
ylim = 0, 6.5; fig.gca().set_ylim(ylim)
mplwp.mark_axeszero(fig.gca())

from scipy.special import gamma
from scipy.optimize import brentq

f1 = lambda x: gamma(1 + x)
x1 = range(4)
y1 = [f1(xx) for xx in x1]
plt.plot(x1, y1, 'o', label='n!', zorder=3)

x2max = brentq(lambda x: f1(x) - ylim[1], 0, xlim[1])
x2 = np.linspace(xlim[0], x2max, 5000)
y2 = [f1(xx) for xx in x2]
plt.plot(x2, y2, label='$\Gamma(n+1)$', zorder=2,
         color=fig.gca().lines[-1].get_color())

f3 = lambda x: sqrt(2*pi*x)*(x/e)**x
x3max = brentq(lambda x: f3(x) - ylim[1], 0, xlim[1])
x3 = np.linspace(0, x3max, 5000)
y3 = [f3(xx) for xx in x3]
plt.plot(x3, y3, label=ur'$\sqrt{2\pi n}(n/e)^n$', zorder=1)

mpl.rc('legend', borderaxespad=1.3)
plt.legend(loc='upper left')
plt.savefig(name)
mplwp.postprocess(name)

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported 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.
You may select the license of your choice.
Annotations
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This image is annotated: View the annotations at Commons

Captions

Comparison of plots of the gamma function and Stirling's approximation

31 January 2015

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current13:04, 12 June 2016Thumbnail for version as of 13:04, 12 June 2016600 × 400 (30 KB)Geek3opaque legend
12:10, 31 January 2015Thumbnail for version as of 12:10, 31 January 2015600 × 400 (30 KB)Geek3factorial_gamma_stirling plot by Geek3

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