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[Bug-gsl] [bug #50711] Gauss hypergeometric function : gsl_sf_hyperg_2F1

From: Patrick Alken
Subject: [Bug-gsl] [bug #50711] Gauss hypergeometric function : gsl_sf_hyperg_2F1 gives up (GSL_EUNIMPL)
Date: Mon, 3 Apr 2017 17:43:45 -0400 (EDT)
User-agent: Mozilla/5.0 (X11; Linux x86_64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/57.0.2987.133 Safari/537.36


                 Summary: Gauss hypergeometric function : gsl_sf_hyperg_2F1
gives up (GSL_EUNIMPL)
                 Project: GNU Scientific Library
            Submitted by: psa
            Submitted on: Mon 03 Apr 2017 09:43:44 PM UTC
                Category: None
                Severity: 3 - Normal
        Operating System: 
                  Status: None
             Assigned to: None
             Open/Closed: Open
         Discussion Lock: Any



from mohammad =dot= alaggan =at= inria =dot= fr


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,


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