KELVIN_KEI0 Function

Evaluates the Kelvin function of the second kind, kei, of order zero.

Usage

result = KELVIN_KEI0(x)

Input Parameters

x—Argument for which the function value is desired.

Returned Value

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

Input Keywords

Double—If present and nonzero, double precision is used.

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.

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 function KELVIN_KEI0 is based on the work of Burgoyne (1963).

If x < 0, NaN (Not a Number) is returned. If x ³ 119, zero is returned.

Example

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

PRINT, KELVIN_KEI0(0.4)

; PV-WAVE prints: -0.703800

PRINT, KELVIN_KEI0(0.6, /DERIVATIVE)

; PV-WAVE prints: 0.348164