IMSL_BESSY

Syntax | Return Value | Arguments | Keywords | Discussion | Example | Version History

The IMSL_BESSY function evaluates a Bessel function of the second kind with real order and real or complex parameters.

Note
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Syntax

Result = IMSL_BESSY(order, z [, /DOUBLE] [, SEQUENCE=value])

Return Value

The desired value of the modified Bessel function.

Arguments

order

Real parameter specifying the desired order. The argument order must be greater than –1/2.

z

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

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 IMSL_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

The IMSL_BESSY function 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 = 0, 3 DO PM, IMSL_BESSY(i + .3, z) 
   ( -0.0131453, 0.379593) 
   (  -0.715533, 0.338082) 
   (   -1.04777, 0.794969) 
   (   -1.62487,  3.68447) 
PM, IMSL_BESSY(.3, z, Sequence = 4), Title = 'With SEQUENCE:' 
With SEQUENCE: 
   ( -0.0131453, 0.379593) 
   (  -0.715533, 0.338082) 
   (   -1.04777, 0.794969) 
   (   -1.62487,  3.68447) 

Version History