Using version 2.6 of GSL from ftp://ftp.gnu.org/gnu/gsl/gsl-2.6.tar.gz

OS is Ubuntu 18.04.2 LTS

Hardware is a Dell workstation with a 3.60 GHz Intel i7-4790 and 32 GB of RAM
 
Compiler is gcc 7.4.0 with the -w option

Descriptions:

when the second argument to gsl_sf_bessel_zero_Jnu is a NaN, that NaN is dropped and the function returns a zero without complaining. The same is true of an inf input.

When the first argument is zero and second argument is a NaN, gsl_sf_hermite returns 1. When the first argument is nonzero, the error handler is invoked as would be expected.

When the first argument is zero and third argument is a NaN, gsl_sf_gegenpoly_n returns 1. When the first argument is nonzero, the error handler is invoked as would be expected.

#include <gsl/gsl_sf.h>
#include <stdio.h>
#include <gsl/gsl_math.h>

int main (void){
double out;

out = gsl_sf_bessel_zero_Jnu(1, GSL_NAN);

printf("%f\n", out);
printf("%.*e\n", out);

out = gsl_sf_hermite(0, GSL_NAN);

printf("%f\n", out);
printf("%.21e\n", out);

out = gsl_sf_gegenpoly_n(0, 2.5, GSL_NAN);

printf("%f\n", out);
printf("%.21e\n", out);
return 0;
}