IDL Analyst Reference Guide: Special Functions

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