from mohammad =dot= alaggan =at= inria =dot= fr
Hello,
I am trying to compute the following function:
gsl_sf_hyperg_2F1(i,n+j,1i+j, x)
for nonnegative 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,
