Dataplot Vol 2 Vol 1

# CGAMMA

Name:
CGAMMA (LET)
Type:
Library Function
Purpose:
Compute the gamma function with complex arguments.
Description:
The complex gamma function is defined as:

where z is a complex number with a positive real component.

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

Syntax 1:
LET <yr> = CGAMMA(<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 gamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

Syntax 2:
LET <yc> = CGAMMAI(<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 gamma values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

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

Examples:
LET A = CGAMMA(1,2)
LET A = CGAMMAI(1,2)

LET YR = CGAMMA(XR,2)
LET YC = CGAMMAI(XR,2)

LET YR = CGAMMA(XR,XC)
LET YC = CGAMMAI(XR,XC)

Note:
Library functions are distinguished from let subcommands in the following ways.
1. Functions enclose the input value in parenthesis. Let subcommands use spaces.

2. Functions can accept (and return) either parameters (i.e., single values) or variables (i.e., an array of values) while let subcommands are specific in which they accept as input and what they return as output.

3. Functions can accept expressions while let subcommands do not. For example, the following is legal:

LET Y2 = ABS(Y1-INT(Y1))

For let subcommands, you typically have to do something like the following:

LET YTEMP = Y**2 + 8
LET A = SUM YTEMP
Default:
None
Synonyms:
None
Related Commands:
 CLNGAM = Compute the complex log 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, pp. 182-184.

"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 5 5 95 95
TITLE AUTOMATIC
PLOT CGAMMA(XR,2) FOR XR = 0.1 0.1 5
PLOT CGAMMA(XR,5) FOR XR = 0.1 0.1 5
PLOT CGAMMAI(XR,2) FOR XR = 0.1 0.1 5
PLOT CGAMMAI(XR,5) FOR XR = 0.1 0.1 5
END OF MULTIPLOT

Date created: 6/5/2001
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.