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## Re: [Help-gsl] ln of gamma function for negative arguments

**From**: |
Inigo Aldazabal Mensa |

**Subject**: |
Re: [Help-gsl] ln of gamma function for negative arguments |

**Date**: |
Thu, 10 Aug 2006 10:55:05 +0200 |

**User-agent**: |
KMail/1.9.1 |

Hi,
You could make use of the relation (say G for Gamma):
G(x)=G(x+1)/x -1<x<0 [1]
and recursively compute Gamma for any negative, non-integer, x.
When first dealing with Gamma function I found this [2] document particulary
useful. You can download a ps version from there.
Regards,
IÃ±igo
[1] Abramowitz and Stegun. Handbook of Mathematical Functions. Eq. 6.1.15
http://www.math.sfu.ca/~cbm/aands/page_256.htm
[2]
http://numbers.computation.free.fr/Constants/Miscellaneous/gammaFunction.html
El Thursday, 10 de August de 2006 04:00, Marc Normandin escribiÃ³:
>* Hello,*
>
>* I require the computation of ln of the gamma function for all negative*
>* non-integer values. The reflection formula can be used for half of the*
>* negative non-integers along with the log since for half the values will be*
>* positive. However, I would like to obtain a value for the other half. I'm*
>* using the ln of gamma as an intermediate step after which I raise the*
>* result with an exponential, so that ultimately I am not after the actual*
>* value of ln gamma itself. I am open to any methods that work.*
>
>* At the current time the only way that I've found to compute the ln of gamma*
>* for negative non-integer values is to treat the argument as a complex*
>* number z = -x + 0i and then use Ln(z) = ln(|z|) + iPI, for the term*
>* involving the sin from the relfection formula.*
>
>* I'd appreciate help and suggestions.*
>
>* Thanks,*
>* Marc.*
>* _______________________________________________*
>* Help-gsl mailing list*
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>* http://lists.gnu.org/mailman/listinfo/help-gsl*