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### IMSL_BESSI_EXP

IMSL_BESSI_EXP

The IMSL_BESSI_EXP function evaluates the exponentially scaled modified Bessel function of the first kind of orders zero and one.

## Syntax

Result = IMSL_BESSI_EXP(order, x [, /DOUBLE])

## Return Value

The value of the exponentially scaled modified Bessel function of the first kind of order zero or one evaluated at 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 is I0(x) is defined to be:

If order is one, the function I1(x) is defined to be:

If order is one then IMSL_BESSI_EXP underflows if |x|/2 underflows.

## Example

The expression e-4.5I0 (4.5) is computed directly by calling IMSL_BESSI_EXP and indirectly by calling IMSL_BESSI. The absolute difference is printed. For large x, the internal scaling provided by IMSL_BESSI_EXP avoids overflow that may occur in IMSL_BESSI.

#### Output

`ans = IMSL_BESSI_EXP(0, 4.5)  error = ABS(ans - EXP(-4.5)*IMSL_BESSI(0, 4.5))  PRINT, ans       0.194198  PRINT, ';Error =', error  Error = 4.4703484e-08  `

## Version History

 6.4 Introduced