File:Mplwp factorial stirling loglog2.svg

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File:Mplwp factorial stirling loglog2.svg

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Original file (SVG file, nominally 600 × 400 pixels, file size: 52 KB)

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Summary

Description

English: Plot of the logarithms of the factorial (gamma function) and Stirling's approximation with two and three terms in the interval [1, 10³] with double-logarithmic scale:

y_{1}(n)=\ln(n!)

y_{2}(n)=n\ln n-n+{\frac {1}{2}}\ln(2\pi n)

y_{2}(n)=n\ln n-n

Date

31 January 2015

Source

Own work

Author

Geek3

Other versions

Mplwp factorial stirling loglog.svg

SVG development

The SVG code is valid.

This plot was created with mplwp, the Matplotlib extension for Wikipedia plots.

Source code

mplwp source code

The plot was generated with mplwp 1.0

#!/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_stirling_loglog2.svg'
fig = mplwp.fig_standard(mpl)

xlim = 1, 1e3; fig.gca().set_xlim(xlim)
ylim = 1e-1, 1e4; fig.gca().set_ylim(ylim)

from scipy.special import gammaln
from scipy.optimize import brentq

f1 = lambda x: gammaln(1 + x)
x1min = brentq(lambda x: f1(x) - ylim[0], xlim[0], xlim[1])
x1 = np.logspace(log10(x1min), log10(xlim[1]), 5000)
y1 = [f1(xx) for xx in x1]
plt.loglog(x1, y1, zorder=3, label='ln n!')

f2 = lambda x: x * log(x) - x + 0.5 * log(2*pi*x)
x2min = brentq(lambda x: f2(x) - ylim[0], xlim[0], xlim[1])
x2 = np.logspace(log10(x2min), log10(xlim[1]), 5000)
y2 = [f2(xx) for xx in x2]
plt.loglog(x2, y2, zorder=2,
           label=ur'n ln n \u2212 $n +\,\frac{1}{2}\,ln(2\pi n)$')

f3 = lambda x: x * log(x) - x
x3min = brentq(lambda x: f3(x) - ylim[0], xlim[0], xlim[1])
x3 = np.logspace(log10(x3min), log10(xlim[1]), 5000)
y3 = [f3(xx) for xx in x3]
plt.loglog(x3, y3, zorder=1, label=u'n ln n \u2212 n')

plt.legend(loc='lower right').get_frame().set_alpha(0.9)
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.

File history

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

	Date/Time	Thumbnail	Dimensions	User	Comment
current	12:43, 31 January 2015		600 × 400 (52 KB)	Geek3	factorial_stirling_loglog2 plot by Geek3

File usage

The following page uses this file:

Factorial

Global file usage

The following other wikis use this file:

Usage on ca.wikipedia.org
- Fórmula de Stirling
Usage on hi.wikipedia.org
- क्रमगुणित
Usage on id.wikipedia.org
- Pengguna:Dedhert.Jr/Uji halaman 01/13

Metadata

This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

If the file has been modified from its original state, some details may not fully reflect the modified file.

Short title	mplwp_factorial_stirling_loglog2.svg
Image title	http://commons.wikimedia.org/wiki/File:mplwp_factorial_stirling_loglog2.svg Plot created with mplwp, the Matplotlib extension for Wikipedia plots.
Width	600px
Height	400px

Retrieved from "https://en.wikipedia.org/wiki/File:Mplwp_factorial_stirling_loglog2.svg"

Summary

mplwp source code

Licensing

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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

File history

File usage

Global file usage

Metadata