bessel_exp_K1

Evaluates the exponentially scaled modified Bessel function of the second kind of order one.

Synopsis

#include <imsl.h>

float imsl_f_bessel_exp_K1 (float x)

The type double function is imsl_d_bessel_exp_K1.

Required Arguments

float x (Input)
Point at which the Bessel function is to be evaluated.

Return Value

The value of the scaled Bessel function exK1(x). If no solution can be computed, NaN is returned.

Description

The result

 

overflows if x is too close to zero. The definition of the Bessel function

 

Example

The expression

 

is computed directly by calling imsl_f_bessel_exp_K1 and indirectly by calling imsl_f_bessel_K1. The absolute difference is printed. For large x, the internal scaling provided by imsl_f_bessel_exp_K1 avoids underflow that may occur in imsl_f_bessel_K1.

 

#include <imsl.h>

#include <stdio.h>

#include <math.h>

 

int main()

{

float x = 0.5;

float ans;

float error;

 

ans = imsl_f_bessel_exp_K1 (x);

printf("(e**0.5)K1(0.5) = %f\n\n", ans);

 

error = fabs(ans - (exp(x)*imsl_f_bessel_K1(x)));

printf ("Error = %e\n", error);

}

Output

 

(e**0.5)K1(0.5) = 2.731010

 

Error = 5.890406e-08