BESSI_EXP Function

Evaluates the exponentially scaled modified Bessel function of the first kind of orders zero and one.

Usage

result = BESSI_EXP(order, x)

Input Parameters

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

x—Argument for which the function value is desired.

Returned Value

result—The value of the exponentially scaled modified Bessel function of the first kind of order zero or one evaluated at x.

Input Keywords

Double—If present and nonzero, double precision is used.

Discussion

If 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 BESSI_EXP underfows if |x|/2 underflows.

Example

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

Output

ans = BESSI_EXP(0, 4.5)

error = ABS(ans - EXP(-4.5)*BESSI(0, 4.5))

PRINT, ans

; PV-WAVE prints: 0.194198

PRINT, 'Error =', error

; PV-WAVE prints: Error = 4.4703484e-08