Hi,
I am having a problem with gsl_sf_hyperg_2F1.
With the parameters (-0.5, 0.5, 1, x) the returned values show a jump at
x=0.5. For x<0.5 the results seem to be correct, while for x>0.5 they
aren't.
The function gsl_sf_hyperg_2F1_e calls hyperg_2F1_series for x<0.5, but
hyperg_2F1_reflect for x>0.5. The latter function checks for c-a-b being
an integer (which it is in my case). If I change one of the parameters
a,b,c by a small amount, the other branch of the function is taken and the
results are correct again.
Unfortunately I know too little about the numerics of 2F1 to suggest a
patch at the moment.