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Dataplot Vol 2 Vol 1

CLNBETA

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

      B(p,q) = INTEGRAL(t**(p-1)*(1-t)**(q-1)dt and the integral is taken from 0 to 1

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

    The complex beta function is simply the natural log of the above function.

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

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

    This syntax computes the real component of the complex log 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.

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

    This syntax computes the complex component of the complex log 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.

Examples:
    LET A = CLNBETA(1,2)
    LET A = CLNBETAI(1,2)

    LET YR = CLNBETA(XR,2)
    LET YC = CLNBETAI(XR,2)

    LET YR = CLNBETA(XR,XC)
    LET YC = CLNBETAI(XR,XC)

Default:
    None
Synonyms:
    None
Related Commands:
    CBETA = Compute the complex beta function.
    CGAMMA = Compute the complex gamma function.
    CLNGAM = Compute the complex log gamma function.
    BETA = Compute the beta function.
    GAMMA = Compute the Gamma function.
    GAMMAI = Compute the incomplete Gamma 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 CLNBETA(XR,2,1,0) FOR XR = 0.1 0.1 5
    PLOT CLNBETA(XR,5,1,0) FOR XR = 0.1 0.1 5
    PLOT CLNBETAI(XR,2,1,1) FOR XR = 0.1 0.1 5
    PLOT CLNBETAI(XR,5,1,1) FOR XR = 0.1 0.1 5
    END OF MULTIPLOT

    plot generated by sample program

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