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7.33 Examples

The following example demonstrates the use of the error handling form of the special functions, in this case to compute the Bessel function J_0(5.0),

#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_sf_bessel.h>

int
main (void)
{
  double x = 5.0;
  gsl_sf_result result;

  double expected = -0.17759677131433830434739701;
  
  int status = gsl_sf_bessel_J0_e (x, &result);

  printf ("status  = %s\n", gsl_strerror(status));
  printf ("J0(5.0) = %.18f\n"
          "      +/- % .18f\n", 
          result.val, result.err);
  printf ("exact   = %.18f\n", expected);
  return status;
}

Here are the results of running the program,

$ ./a.out 
status  = success
J0(5.0) = -0.177596771314338292 
      +/-  0.000000000000000193
exact   = -0.177596771314338292

The next program computes the same quantity using the natural form of the function. In this case the error term result.err and return status are not accessible.

#include <stdio.h>
#include <gsl/gsl_sf_bessel.h>

int
main (void)
{
  double x = 5.0;
  double expected = -0.17759677131433830434739701;
  
  double y = gsl_sf_bessel_J0 (x);

  printf ("J0(5.0) = %.18f\n", y);
  printf ("exact   = %.18f\n", expected);
  return 0;
}

The results of the function are the same,

$ ./a.out 
J0(5.0) = -0.177596771314338292
exact   = -0.177596771314338292