BESSI Function

Evaluates a modified Bessel function of the first kind with real order and real or complex parameters.

Usage

result = BESSI(order, z)

Input Parameters

order—Real parameter specifying the desired order. Parameter order must be greater than –1/2.

z—Real or complex parameter for which the Bessel function is to be evaluated.

Returned Value

result—The desired value of the modified Bessel function.

Input Keywords

Double—If present and nonzero, double precision is used.

Sequence—If present and nonzero, a one-dimensional array of length n containing the values of the Bessel function through the series is returned by BESSI, where n = N_ELEMENTS(Sequence). The i^th element of this array is the Bessel function of order (order + i) at z for i = 0, ... (n – 1).

Discussion

Function BESSI evaluates a modified Bessel function of the first kind with real order and real or complex parameters. The data type of the returned value is always complex.

The Bessel function, I_v(z), is defined as follows:

 

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

Example

In this example, J_{0.3 + v–1}(1.2 + 0.5i), v = 1, ... 4 is computed and printed first by calling BESSI four times in a row, then by using the keyword Sequence.

z = COMPLEX(1.2, .5)

FOR i=0L, 3 DO PM, BESSI(i + .3, z)

; PV-WAVE prints the following:

; (    1.16339,  0.396301)

; (   0.447264,  0.332142)

; (  0.0821799,  0.127165)

; ( 0.00577678, 0.0286277)

PM, BESSI(.3, z, Sequence = 4), Title = 'With SEQUENCE:'

; PV-WAVE prints the following:

; With SEQUENCE:

; (    1.16339,  0.396301)

; (   0.447264,  0.332142)

; (  0.0821799,  0.127165)

; ( 0.00577678, 0.0286277)