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

[Patrick Alken]

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.

Thanks,
Patrick

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