bessel_Ix

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

Synopsis

#include <imsl.h>

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

The type d_complex function is imsl_z_bessel_Ix.

Required Arguments

float xnu (Input)
The lowest order desired. 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_Ix (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 Iv(z) is defined to be

 

For large arguments, z, Temme’s (1975) algorithm is used to find Iv(z). The Iv(z) values are recurred upward (if this is stable). This involves evaluating a continued fraction. If this evaluation fails to converge, the answer may not be accurate.

For moderate and small arguments, Miller’s method is used.

Example

In this example, J0.3+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_Ix(xnu, z, n, 0);

 

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

printf("I 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

 

I sub 0.30 ((1.20,0.50)) =(1.163,0.396)

I sub 1.30 ((1.20,0.50)) =(0.447,0.332)

I sub 2.30 ((1.20,0.50)) =(0.082,0.127)

I sub 3.30 ((1.20,0.50)) =(0.006,0.029)