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### IMSL_BESSK_EXP

IMSL_BESSK_EXP

The IMSL_BESSK_EXP function evaluates the exponentially scaled modified Bessel function of the third kind of orders zero and one.

If the argument Order is zero, the Bessel function K0(x) is defined to be:

If order is one, the value of the Bessel function K1(x):

The argument X must be greater than zero for the result to be defined.

## Example

The expression:

is computed directly by calling IMSL_BESSK_EXP, and indirectly by calling IMSL_BESSK. The absolute difference is printed. For large x, the internal scaling provided by IMSL_BESSK_EXP avoids underflow that may occur in IMSL_BESSK.

`ans = IMSL_BESSK_EXP(0, 0.5)`
`error = ABS(ans - (EXP(0.5))*IMSL_BESSK(0, 0.5)) PRINT, ans`
`  1.52411`
`PRINT, 'Error =', error`

IDL prints:

`Error = 1.1920929e-07`

## Errors

### Fatal Errors

MATH_SMALL_ARG_OVERFLOW: The argument X must be large enough (X > max (1/b, s) where s is the smallest representable positive number and b is the largest representable number) that K1(X) does not overflow.

## Syntax

Result = IMSL_BESSK_EXP(Order, X [, /DOUBLE])

## Return Value

The value of the exponentially scaled Bessel function exK0(x) or exK1(x)

## Arguments

### Order

Order of the function. The order must be either zero or one.

### X

Argument for which the function value is desired.

## Keyword

### DOUBLE (optional)

If present and nonzero, then double precision is used.

## Version History

 6.4 Introduced