Hypergeometric1F1 for large arguments

Question

I am trying to use the gsl library for calculating 1F1. I have some C code.

The following works and matches Mathematica's results for small real arguments z but not large arguments:

/* file 1F1.c */
#include <stdio.h>
#include <stdlib.h>

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

double _1F1( double b,
            double c,
            double z)
{
    double Fa = gsl_sf_hyperg_1F1(b, c, z);
    return Fa;
}

int main()
{

  double b = 100000.0;
  double c = 14.0;
  double z = 0.9;
  double result;   
  
  result = _1F1(b, c, z);
  printf("1F1(%.1f, %.1f, %.1f): %e\n", b, c, z, result);

  /* result = 3.2042*10^236 in Mathematica*/

  z = 10*z;

  result = _1F1(b, c, z);
  printf("1F1(%.1f, %.1f, %.1f): %e\n", b, c, z, result);       

  /* result = 9.52444189237289*10^794 in Mathematica*/

  return 0;
}

I get:

$    gcc -std=c17 -Wall -pedantic 1F1.c -lm -lgsl -lcblas; ./a.out
1F1(100000.0, 14.0, 0.9): 3.204195e+236
1F1(100000.0, 14.0, 9.0): -nan

So,how do I get around and evaluate for large z, as Mathematica seems to be able to do? I also tried using the Cephes library version, and got into the same problem.

Why does Mathematica not have this problem? They must be using some other formula for large arguments.