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### IMSL_KELVIN_KEI0

IMSL_KELVIN_KEI0

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

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`

## 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 (optional)

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 (optional)

If present and nonzero, then double precision is used.

## Version History

 6.4 Introduced