File:Mplwp factorial gamma stirling.svg

Summary

Description

English: Plot of the factorial, gamma function and Stirling's approximation in the interval [−0.2, 3.2]:

y_{1}(n)=n!

y_{2}(n)=\Gamma (n+1)

y_{3}(n)={\sqrt {2\pi n}}(n/e)^{n}

Date

31 January 2015

Source

Own work

Author

Geek3

Other versions

Mplwp gamma stirling.svg

SVG development

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.

Quality image

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Source code

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:

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.

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

This image is annotated: View the annotations at Commons

	Date/Time	Thumbnail	Dimensions	User	Comment
current	13:04, 12 June 2016		600 × 400 (30 KB)	Geek3	opaque legend
	12:10, 31 January 2015		600 × 400 (30 KB)	Geek3	factorial_gamma_stirling plot by Geek3

Short title	mplwp_factorial_gamma_stirling.svg
Image title	http://commons.wikimedia.org/wiki/File:mplwp_factorial_gamma_stirling.svg Plot created with mplwp, the Matplotlib extension for Wikipedia plots.
Width	600px
Height	400px

File:Mplwp factorial gamma stirling.svg

Summary

mplwp source code

Licensing

Captions

Items portrayed in this file

depicts

factorial

Stirling's approximation

gamma function

gamma function

Stirling's approximation

factorial

creator

some value

copyright status

copyrighted

copyright license

GNU Free Documentation License, version 1.2 or later

Creative Commons Attribution 3.0 Unported

inception

31 January 2015

source of file

original creation by uploader

Commons quality assessment

Wikimedia Commons quality image

File history

File usage

Global file usage

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