The bug I am reporting arose when I tried to the gsl package in R:
gsl: wrapper for the Gnu Scientific Library
The authors of the gsl package have determined that the error is in the Gnu
Scientific Library.
The problem arises with the generalized hypergeometric function and is
illustrated
in the code below. Please excuse my odd syntax where I used 1+9 etc instead of
10
etc. Both Mathematica and MatLab get the result correct.
Browse[2]> hyperg_2F1(-0.2,-0.2 + 9,1 + 9,0.8)
[1] 0.7799897
Browse[2]> hyperg_2F1(-0.2,-0.2 + 10,1 + 10,0.8)
[1] NaN
MATHEMATICA GETS IT CORRECT
Hypergeometric2F1[-0.2, -0.2+9, 1+9, 0.8]
0.77999
Hypergeometric2F1[-0.2, -0.2+10, 1+10, 0.8]
0.775746
MATLAB GETS IT CORRECT
>> hypergeom([-0.2,-0.2+9],1+9,0.8)
ans =
0.7800
>> hypergeom([-0.2,-0.2+10],1+10,0.8)
ans =
0.7757
