bessel_Kx

Evaluates a sequence of modified Bessel functions of the second kind with real order and complex arguments.

Synopsis

#include <imsl.h>

f_complex *imsl_c_bessel_Kx (float xnu, f_complex z, int n, …, 0)

The type d_complex function is imsl_z_bessel_Jx.

Required Arguments

float xnu (Input)
The lowest order desired. The argument xnu must be greater than −1/2.

f_complex z (Input)
Argument for which the sequence of Bessel functions is to be evaluated.

int n (Input)
Number of elements in the sequence.

Return Value

A pointer to the n values of the function through the series. Element i contains the value of the Bessel function of order xnu + i for i = 0, …, n − 1.

Synopsis with Optional Arguments

#include <imsl.h>

f_complex *imsl_c_bessel_Kx (float xnu, f_complex z, int n,

IMSL_RETURN_USER, f_complex bessel[],

0)

Optional Arguments

IMSL_RETURN_USER, f_complex bessel[] (Output)
Store the sequence of Bessel functions in the user-provided array bessel[].

Description

The Bessel function Kv(z) is defined to be

 

This function is based on the code BESSCC of Barnett (1981) and Thompson and Barnett (1987).

For moderate or large arguments, z, Temme’s (1975) algorithm is used to find Kv(z). This involves evaluating a continued fraction. If this evaluation fails to converge, the answer may not be accurate. For small z, a Neumann series is used to compute Kv(z). Upward recurrence of the Kv(z) is always stable.

Example

In this example, K0.3+n-1 (1.2 + 0.5i), ν = 1, …, 4 is computed and printed.

 

#include <imsl.h>

#include <stdio.h>

 

int main()

{

int n = 4;

int i;

float xnu = 0.3;

static f_complex z = {1.2, 0.5};

f_complex *sequence;

 

sequence = imsl_c_bessel_Kx(xnu, z, n, 0);

 

for (i = 0; i < n; i++)

printf("K sub %4.2f ((%4.2f,%4.2f)) = (%5.3f,%5.3f)\n",

xnu+i, z.re, z.im, sequence[i].re, sequence[i].im);

}

Output

 

K sub 0.30 ((1.20,0.50)) = (0.246,-0.200)

K sub 1.30 ((1.20,0.50)) = (0.336,-0.362)

K sub 2.30 ((1.20,0.50)) = (0.587,-1.126)

K sub 3.30 ((1.20,0.50)) = (0.719,-4.839)