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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.

This routine requires an IDL Advanced Math and Stats license. For more information, contact your sales or technical support representative.

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

## See Also

IMSL_KELVIN_BEI0, IMSL_KELVIN_BER0, IMSL_KELVIN_KER0

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