Evaluates the real modified Bessel function of the second kind of order one K1(x).

Synopsis

#include <imsl.h>

float imsl_f_bessel_K1 (float x)

The type double procedure is imsl_d_bessel_K1.

Required Arguments

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

Return Value

The value of the Bessel function

If no solution can be computed, NaN is returned.

Description

Since K1(x) is complex for negative x and is undefined at x = 0, imsl_f_bessel_K1 is defined only for x > 0. For large x, imsl_f_bessel_K1 will underflow.
See Figure 9-12 for a graph of K1(x).

Example

The Bessel function K1(1.5) is evaluated.

#include <imsl.h>

main()
{
    float       x = 1.5;
    float       ans;

    ans = imsl_f_bessel_K1(x);
    printf("K1(%f) = %f\n", x, ans);
}

Output

K1(1.500000) = 0.277388

Alert Errors

IMSL_LARGE_ARG_UNDERFLOW                The argument x must not be so large that the result, approximately equal to,

                                                                                     underflows.

Fatal Errors

IMSL_SMALL_ARG_OVERFLOW                  The argument x must be large enough (x > max (1/b, s) where s is the smallest representable positive number and b is the largest repesentable number) that K1(x) does not overflow.

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