IMSL_BESSK

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

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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:'

IDL prints:

With SEQUENCE:

( 0.245546, -0.199599)

( 0.335637, -0.362005)

( 0.586718, -1.12610)

( 0.719456, -4.83864)

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 (optional)

If present and nonzero, then 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).

Version History

6.4	Introduced