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

When attempting to evaluate the limit approaching positive infinity,
the scaled irregular modified cylindrical Bessel function reduces to
an indeterminate form of 0 x inf but GSL just returns a zero without
complaining

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

int main (void){
        double out;
        out = gsl_sf_bessel_Kn_scaled(0, GSL_POSINF);

        printf("%.*f\n", DBL_DIG-1, out);
        printf("%.21e\n", out);
        return 0;
}