[Help-gsl] Gauss hypergeometric function : gsl_sf_hyperg_2F1 gives up (GSL_EUNIMPL)

[Mohammad Alaggan]

Hello,

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