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 <math.h>

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

 

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