bessel_exp_K0
Evaluates the exponentially scaled modified Bessel function of the second kind of order zero.
Synopsis
#include <imsl.h>
float imsl_f_bessel_exp_K0 (float x)
The type double function is imsl_d_bessel_exp_K0.
Required Arguments
float x (Input)
Point at which the Bessel function is to be evaluated.
Return Value
The value of the scaled Bessel function exK0(x). If no solution can be computed, NaN is returned.
Description
The argument must be greater than zero for the result to be defined. The Bessel function K0(x) is defined to be
Example
The expression
is computed directly by calling imsl_f_bessel_exp_K0 and indirectly by calling imsl_f_bessel_K0. The absolute difference is printed. For large x, the internal scaling provided by imsl_f_bessel_exp_K0 avoids underflow that may occur in imsl_f_bessel_K0.
#include <imsl.h>
#include <stdio.h>
#include <math.h>
int main()
{
float x = 0.5;
float ans;
float error;
ans = imsl_f_bessel_exp_K0 (x);
printf("(e**0.5)K0(0.5) = %f\n\n", ans);
error = fabs(ans - (exp(x)*imsl_f_bessel_K0(x)));
printf ("Error = %e\n", error);
}
Output
(e**0.5)K0(0.5) = 1.524109
Error = 2.028498e-08
