Hypergeometric function

[Michal Sprlak]

Dear Madam/Sir,

I have been using GSL for a couple of years. Most recently, I have used the
hypergeometric functions in my computations, namely the
function gsl_sf_hyperg_2F1.

I have found that this function results in an error (GSL ver. 2.7, and the
same happens in ver. 2.1):
gsl: hyperg_2F1.c:773: ERROR: error
Default GSL error handler invoked.
Aborted (core dumped)

I get this message when calculating:
gsl_sf_hyperg_2F1(0.5 * (m - n), - 0.5 * (m + n), 0.5 * (1.0 - 2.0 * n),
aux1),
with m=0, n=37, aux1 = 2.14041375888928714E-01;
or with m=0, n=126, aux1 = 6.37430876026404275E-02.

For m=0, n=172, aux1 = 2.93703482001987093E-02; I get a different message:
gsl: exp.c:254: ERROR: overflow
Default GSL error handler invoked.
Aborted (core dumped)

I run GSL on Ubuntu Release 16.04.7 LTS (Xenial Xerus) 64-bit, Kernel Linux
4.4.0-210-generic x86_64, Intel® Core™ i5-6198DU CPU @ 2.30GHz × 4.

I tried the same computations in different programs implementing
calculation of the Gauss hypergeometric function for the same parameters
and the results were consistent (e.g. in Matlab and in Mathcad).

Do you think there could be a way to fix this problem? I would like to use
GSL in the future for some high values of n and m (reaching a few thousand
if possible).

Best regards,
Michal Sprlak