IMSL_KELVIN_KER0

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

The KELVIN_KERO function evaluates the Kelvin function of the second kind, ker, of order zero.

Note
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Syntax

Result = IMSL_KELVIN_KER0(x [, DERIVATIVE=value] [, /DOUBLE])

Return Value

The value of the Kelvin function of the second kind, ker, of order zero evaluated at x.

Arguments

x

Argument for which the function value is desired.

Keywords

DERIVATIVE

If present and nonzero, then the derivative of the Kelvin function of the second kind, ker, of order zero evaluated at x is computed.

DOUBLE

If present and nonzero, double precision is used.

Discussion

The modified Kelvin function ker₀(x) is defined to be ¬K₀(xe^pi/4). The Bessel function K₀(x) is defined:

If the keyword DERIVATIVE is set, the function ker₀′(x) is defined to be:

If x < 0, NaN (Not a Number) is returned. If x ≥ 119, then zero is returned.

The IMSL_KELVIN_KER0 function is based on the work of Burgoyne (1963).

Example

In this example, ker₀(0.4) and ker₀′(0.6) are evaluated.

PRINT, IMSL_KELVIN_KER0(0.4) 
      1.06262 
PRINT, IMSL_KELVIN_KER0(0.6, /DERIVATIVE) 
     -1.45654 

Version History