URL:
<http://savannah.gnu.org/bugs/?28718>
Summary: gsl_sf_hyperg_1F1(-1.5,1.5,-100) catastrophic
cancellation in series
Project: GNU Scientific Library
Submitted by: bjg
Submitted on: Sat 23 Jan 2010 02:09:25 PM GMT
Category: Accuracy problem
Severity: 3 - Normal
Operating System:
Status: Confirmed
Assigned to: bjg
Open/Closed: Open
Release: 1.13
Discussion Lock: Any
_______________________________________________________
Details:
From: Lorenzo Moneta <[email protected]>
To: <[email protected]>
CC: Weibin Li <[email protected]>, Brian Gough
<[email protected]>
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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