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Re: [Help-gsl] Gauss hypergeometric function : gsl_sf_hyperg_2F1 gives u

From: Patrick Alken
Subject: Re: [Help-gsl] Gauss hypergeometric function : gsl_sf_hyperg_2F1 gives up (GSL_EUNIMPL)
Date: Mon, 3 Apr 2017 15:44:58 -0600
User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:45.0) Gecko/20100101 Thunderbird/45.8.0

Hello, thanks for your report. I have logged the issue into the bug tracker, but unfortunately it may be some time before I or someone can look at this - I am not an expert on the hypergeometric functions. If you happen to investigate further and find a fix I would be happy to apply it.


On 02/19/2017 06:02 AM, Mohammad Alaggan wrote:

I am trying to compute the following function:

gsl_sf_hyperg_2F1(-i,-n+j,1-i+j, x)

for non-negative integers i, j, and n, and real x in (0, 1). In particular, n is at 
least 1 and is usually below 20, and i, j <= n. To help get a result I use the 
symmetry j = n - j, i = n - i, when j < i.

However, the function refuses to compute a result when n = 14 (the case I tried. 
It probably would do the same for n > 10). I am using GSL 2.2.1 and the line 
producing the error is 773 in the file hyperg_2F1.c. The comment there says « We 
give up » . On the other hand, Mathematica can successfully compute the value as 
shown in the example below.

Example inputs (with associated Mathematica output):

gsl_sf_hyperg_2F1(-1, -13, 1, 0.651439) = 9.46871
gsl_sf_hyperg_2F1(0 , -11, 4, 0.651439) = 1

I am using this function to compute the transition probability between n 
states, and n may be as large as 20.

Thank you,

Mohammad Alaggan,
Postdoctoral Researcher
Team Privatics
Inria Lyon, France

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