IMSL_BESSK

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

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

Note
This routine requires an IDL Advanced Math and Stats license. For more information, contact your ITT Visual Information Solutions sales or technical support representative.

Syntax

Result = IMSL_BESSK(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_BESSK, 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_BESSK function evaluates a modified 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, K_v(z), is defined as follows:

This function is based on the code BESSCC of Thompson (1981) and Thompson and Barnett (1987). For moderate or large parameters, z, Temme's (1975) algorithm is used to find K_v (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 K_v (z). Upward recurrence of the K_v (z) is always stable.

Example

In this example, K_{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_BESSK(i + .3, z) 
   ( 0.245546, -0.199599) 
   ( 0.335637, -0.362005) 
   ( 0.586718,  -1.12610) 
   ( 0.719457,  -4.83864) 
PM, IMSL_BESSK(.3, z, Sequence = 4), Title = 'With SEQUENCE:' 
With SEQUENCE: 
   ( 0.245546, -0.199599) 
   ( 0.335637, -0.362005) 
   ( 0.586718,  -1.12610) 
   ( 0.719456,  -4.83864) 

Version History