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### IMSL_KELVIN_BEI0

IMSL_KELVIN_BEI0

The IMSL_KELVIN_BEI0 function evaluates the Kelvin function of the first kind, bei, of order zero.

The Kelvin function bie0(x) is defined to be . The Bessel function J0(x) is defined:

In IMSL_KELVIN_BEI0, x must be less than 119.

If the keyword DERIVATIVE is set, the function bei0′(x) is defined to be:

If the keyword DERIVATIVE is set and |x| > 119, NaN is returned.

The IMSL_KELVIN_BEI0 function is based on the work of Burgoyne (1963).

## Example

In this example, bei0(0.4) and bei0′(0.6) are evaluated.

`PRINT, IMSL_KELVIN_BEI0(0.4)`
`  0.0399982`
`PRINT, IMSL_KELVIN_BEI0(0.6, /DERIVATIVE)`
`  0.299798`

## Syntax

Result = IMSL_KELVIN_BEI0(X [, DERIVATIVE=value] [, /DOUBLE])

## Return Value

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

### DOUBLE (optional)

If present and nonzero, then double precision is used.

## Version History

 6.4 Introduced