BESSY Function

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

Usage

result = BESSY(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 BESSY, where n = NELEMENTS(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 BESSY evaluates a Bessel function of the second kind with real order and real or complex parameters. The data type of the returned value is always complex.

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

 

 

This function is based on the code BESSCC of Thompson (1981) and Thompson and Barnett (1987). This code computes Y_v(z) from the modified Bessel functions I_v(z) and K_v(z), using the following relation:

 

Example

In this example, Y_{0.3 + v–1}(1.2 + 0.5i), v = 1, ..., 4 is computed and printed.

z = COMPLEX(1.2, .5)

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

; PV-WAVE prints the following:

;   ( -0.0131453, 0.379593)

;   (  -0.715533, 0.338082)

;   (   -1.04777, 0.794969)

;   (   -1.62487,  3.68447)

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

; PV-WAVE prints the following:

;   With SEQUENCE:

;   ( -0.0131453, 0.379593)

;   (  -0.715533, 0.338082)

;   (   -1.04777, 0.794969)

;   (   -1.62487,  3.68447)