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User's guide for special functions now reports accuracy of 

Gamma.logGamma(double).


git-svn-id: https://svn.apache.org/repos/asf/commons/proper/math/trunk@1392739 13f79535-47bb-0310-9956-ffa450edef68
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Sebastien Brisard 2012-10-02 05:00:41 +00:00
parent 57b0a07b9f
commit d685138370
1 changed files with 28 additions and 9 deletions
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37
src/site/apt/userguide/special.apt
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@ -39,16 +39,35 @@
* 5.3 Gamma functions
{{{../apidocs/org/apache/commons/math3/special/Gamma.html}Gamma}} contains
several useful functions involving the Gamma Function.
Class {{{../apidocs/org/apache/commons/math3/special/Gamma.html}<<<Gamma>>>}}
contains several useful functions involving the Gamma Function.
*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
|| Function || Method || Reference |
*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
| Log Gamma | logGamma | See {{{http://mathworld.wolfram.com/GammaFunction.html}Gamma Function}} from MathWorld |
*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
| Regularized Gamma | regularizedGammaP | See {{{http://mathworld.wolfram.com/RegularizedGammaFunction.html}Regularized Gamma Function}} from MathWorld |
*-------------------+-------------------+---------------------------------------------------------------------------------------------------------------+
** 5.3.1 Log Gamma
<<<Gamma.logGamma(x)>>> computes the natural logarithm of the Gamma function,
log \u0393(x), for x > 0
(see {{{http://mathworld.wolfram.com/LogGammaFunction.html}MathWorld}},
{{{http://dlmf.nist.gov/5}DLMF}}). The accuracy of the Commons-Math
implementation is assessed by comparaison with high precision values computed
with the {{{http://maxima.sourceforge.net/}Maxima}} Computer Algebra System.
*---------------------------------------------+---------------------------------------+-----------------+----------------+
|| Interval || Values tested || Average error || Maximum error |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
| (0.0, 8.0] | <<<k / 1024, k = 1, ..., 8192>>> | 0.32 ulps | 4.0 ulps |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
| (8.0, 1024.0] | <<<k / 8, k = 65, ..., 8192>>> | 0.43 ulps | 3.0 ulps |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
| (1024.0, 8192.0] | <<<k, k = 1025, 8192>>> | 0.53 ulps | 3.0 ulps |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
| [8933.439345993791, 1.75555970201398e+305] | <<<2**(k / 8), k = 105, ..., 8112>>> | 0.35 ulps | 2.0 ulps |
*---------------------------------------------+---------------------------------------+-----------------+----------------+
** 5.3.2 Regularized Gamma
<<<Gamma.regularizedGammaP(a, x)>>> computes the value of the regularized
Gamma function, P(a, x)
(see {{{http://mathworld.wolfram.com/RegularizedGammaFunction.html}MathWorld}}).
* 5.4 Beta funtions