CBETA

CBETA (LET)

Library Function

Compute the beta function with complex arguments.

The complex beta function is defined as:

where p and q are complex numbers with positive real components.

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

LET <yr> = CBETA(<pr>,<pc>,<qr>,<qc>)
            <SUBSET/EXCEPT/FOR qualification>
where <pr> is a variable, number, or parameter containing positive values;
            <pc> is a variable, number, or parameter; positive values;
            <qr> is a variable, number, or parameter containing positive values;
            <qc> 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 beta values are stored;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the real component of the complex beta function. The <pr> and <pc> values are the real and complex components of the first input argument respectively and the <qr> and <qc> values are the real and complex components of the second input argument respectively.

LET <yc> = CBETA(<pr>,<pc>,<qr>,<qc>)
            <SUBSET/EXCEPT/FOR qualification>
where <pr> is a variable, number, or parameter containing positive values;
            <pc> is a variable, number, or parameter; positive values;
            <qr> is a variable, number, or parameter containing positive values;
            <qc> 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 beta values are stored; and where the <SUBSET/EXCEPT/FOR qualification> is optional.

This syntax computes the complex component of the complex beta function. The <pr> and <pc> values are the real and complex components of the first input argument respectively and the <qr> and <qc> values are the real and complex components of the second input argument respectively.

LET A = CBETA(1,2)
LET A = CBETAI(1,2)


LET YR = CBETA(XR,2)
LET YC = CBETAI(XR,2)


LET YR = CBETA(XR,XC)
LET YC = CBETAI(XR,XC)

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
   

None

None

CLNBETA	= Compute the complex log beta function.
CLNGAM	= Compute the complex log gamma function.
BETA	= Compute the beta function.
GAMMA	= Compute the Gamma function.
GAMMAI	= Compute the incomplete Gamma function.

"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).

Special Functions

1997/12

MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES
TITLE AUTOMATIC
PLOT CBETA(XR,2,1,0) FOR XR = 0.1 0.1 5
PLOT CBETA(XR,5,1,0) FOR XR = 0.1 0.1 5
PLOT CBETAI(XR,2,1,1) FOR XR = 0.1 0.1 5
PLOT CBETAI(XR,5,1,1) FOR XR = 0.1 0.1 5
END OF MULTIPLOT