IDL Analyst Reference Guide: Special Functions

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 e^xK₀(x) or e^xK₁(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