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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.

## 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.

## Keywords

#### DOUBLE

If present and nonzero, double precision is used.

## Discussion

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  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.

## Version History

 6.4 Introduced

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