Sat 23 Jan 2010 02:09:25 PM UTC, original submission:
From: Lorenzo Moneta <Lorenzo.Moneta@cern.ch>
To: <bug-gsl@gnu.org>
CC: Weibin Li <weibinli@mpipks-dresden.mpg.de>, Brian Gough <bjg@network-theory.co.uk>
Subject: Re: [Bug-gsl] gsl_sf_hyperg_1F1
Date: Thu, 21 Jan 2010 16:12:45 +0100
Hello,
I have found a similar problem, probably related to the inaccuracy in the series calculation of
the hypergeometric function for
gsl_sf_hyperg_1F1( a < 0, b > 0, x << 0).
For example :
gsl_sf_hyperg_1F1(-1.5, 1.5, - 99.9) returns the correct value of 4.55768964383819423e+02
while gsl_sf_hyperg_1F1(-1.5, 1.5, -100.) returns -1.13760e+20 when the correct value is 456.44 (from Mathematica)
I think the Kummer formula ( 1F1(a,b,x) = exp(-x) * 1F1(b-a,b,-x) could be used for larger value of |x| ( at least works for |x| = 700), while
the current cut-off is for |x| < 100.
Best Regards
Lorenzo
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