Evaluates the real modified Bessel function of the second kind of order one K1(x).
Synopsis
#include<imsl.h>
floatimsl_f_bessel_K1 (floatx)
The type double procedure is imsl_d_bessel_K1.
Required Arguments
floatx (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>
#include <stdio.h>
int 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.