[Bug-gsl] gsl_sf_coulomb_wave_FG_e returns NaN but with success flag

[Jens Søren Sieg Svensmark]

Hi

For certain parameters the gsl_sf_coulomb_wave_FG_e returns a NaN value
for Gp (the derivative of the irregular Coulomb function), but the
function does not throw an error.

The problem seems to be similar to bug #30885.

I used gsl 1.16, from the repositories of Ubuntu 15.10.

The following example program

#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_coulomb.h>
int
main (void)
{
  gsl_sf_result F,G,Fp,Gp;
  double exp_F,exp_G;
  double eta=340;
  double L=0;
  double x=48.524525790349422;

  int iret = gsl_sf_coulomb_wave_FG_e
(eta,x,L,0,&F,&Fp,&G,&Gp,&exp_F,&exp_G);
 
  printf ("status  = %s\n", gsl_strerror(iret));
  printf ("F = %.18e\n"
          "      +/- % .18e\n",
          F.val, F.err);
  printf ("Fp = %.18e\n"
          "      +/- % .18e\n",
          Fp.val, Fp.err);
  printf ("G = %.18e\n"
          "      +/- % .18e\n",
          G.val, G.err);
  printf ("Gp = %.18e\n"
          "      +/- % .18e\n",
          Gp.val, Gp.err);
  return iret;
}



Gives the following output:

status  = success
F = 2.593734965617792327e-309
      +/-  2.593734965617787386e-312
Fp = 9.371127281856027958e-309
      +/-  9.371127281859619815e-312
G = 5.343744177206742137e+307
      +/-  5.343744177206741934e+304
Gp = -nan
      +/-  inf