IMSL_KELVIN_KEI0

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

The IMSL_KELVIN_KEI0 function evaluates the Kelvin function of the second kind, kei, of order zero.

Note
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Syntax

Result = IMSL_KELVIN_KEI0(x [, DERIVATIVE=value] [, /DOUBLE])

Return Value

The value of the Kelvin function of the second kind, kei, 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, kei, of order zero evaluated at x is computed.

DOUBLE

If present and nonzero, double precision is used.

Discussion

The modified Kelvin function kei₀(x) is defined to be . The Bessel function K₀(x) is defined as:

If the keyword DERIVATIVE is set, the function kei₀′(x) is defined to be:

The IMSL_KELVIN_KEI0 function is based on the work of Burgoyne (1963).

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

Example

In this example, kei₀(0.4) and kei₀′(0.6) are evaluated.

PRINT, IMSL_KELVIN_KEI0(0.4) 
    -0.703800 
PRINT, IMSL_KELVIN_KEI0(0.6, /DERIVATIVE) 
     0.348164 

Version History