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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
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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.



[1] Abramowitz and Stegun. Handbook of Mathematical Functions. Eq. 6.1.15

El Thursday, 10 de August de 2006 04:00, Marc Normandin escribió:
> 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.
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