 Dataplot Vol 2 Vol 1

# CLNGAM

Name:
CLNGAM (LET)
Type:
Library Function
Purpose:
Compute the log gamma function with complex arguments.
Description:
The complex gamma function is defined as: where z is a complex number with a positive real component.

The log gamma function is simply the natural logarithm of the above function. It is frequently used in computations instead of the complex gamma function because it is less subject to overflow problems.

Dataplot computes this function using the CLNGAM routines from "Computation of Special Functions" (see the References section below).

Syntax 1:
LET <yr> = CLNGAM(<xr>,<xc>)             <SUBSET/EXCEPT/FOR qualification> where <xr> is a variable, number, or parameter containing positive values;
<xc> is a variable, number, or parameter; positive values;
<yr> is a variable or a parameter (depending on what <xr> and <xc> are) where the computed log gamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the real component of the complex log gamma function. The and values are the real and complex components of the input argument respectively.

Syntax 2:
LET <yc> = CLNGAMI(<xr>,<xc>)             <SUBSET/EXCEPT/FOR qualification> where <xr> is a variable, number, or parameter containing positive values;
<xc> is a variable, number, or parameter; positive values;
<yr> is a variable or a parameter (depending on what <xr> and <xc> are) where the computed log gamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the complex component of the complex log gamma function. The and values are the real and complex components of the input argument respectively.

Examples:
LET A = CLNGAM(1,2)
LET A = CLNGAMI(1,2)

LET YR = CLNGAM(XR,2)
LET YC = CLNGAMI(XR,2)

LET YR = CLNGAM(XR,XC)
LET YC = CLNGAMI(XR,XC)

Default:
None
Synonyms:
None
Related Commands:
 CGAMMA = Compute the complex gamma function. CBETA = Compute the complex beta function. CLNBETA = Compute the complex log beta function. GAMMA = Compute the Gamma function. GAMMAI = Compute the incomplete Gamma function. DIGAMMA = Compute the digamma function.
Reference:
"Computation of Special Functions", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, chapter 1.

"Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 1964 (chapter 6).

Applications:
Special Functions
Implementation Date:
1997/12
Program:
MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES
TITLE AUTOMATIC
PLOT CLNGAM(XR,2) FOR XR = 0.1 0.1 5
PLOT CLNGAM(XR,5) FOR XR = 0.1 0.1 5
PLOT CLNGAMI(XR,2) FOR XR = 0.1 0.1 5
PLOT CLNGAMI(XR,5) FOR XR = 0.1 0.1 5
END OF MULTIPLOT

Date created: 6/5/2001
Last updated: 4/4/2003