 Dataplot Vol 2 Vol 1

# CPSI

Name:
CPSI (LET)
Type:
Library Function
Purpose:
Compute the psi (or digamma) function with complex arguments.
Description:
The complex psi function is defined as: where z is a complex number with a positive real component, is the gamma function, and is the derivative of the gamma function.

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

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

This syntax computes the real component of the complex psi function. The <xr> and <xc> values are the real and complex components of the input argument respectively.

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

This syntax computes the complex component of the complex psi function. The <xr> and <xc> values are the real and complex components of the input argument respectively.

Examples:
LET A = CPSI(1,2)
LET A = CPSII(1,2)

LET YR = CPSI(XR,2)
LET YC = CPSII(XR,2)

LET YR = CPSI(XR,XC)
LET YC = CPSII(XR,XC)

Default:
None
Synonyms:
None
Related Commands:
 DIGAMMA = Compute the digamma function. GAMMA = Compute the Gamma function. GAMMAI = Compute the incomplete Gamma function. CGAMMA = Compute the complex gamma function. CLNGAM = Compute the complex log gamma function. CBETA = Compute the complex beta function. CLNBETA = Compute the complex log beta 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
TITLE AUTOMATIC
PLOT CPSI(XR,2) FOR XR = 0.1 0.1 5
PLOT CPSI(XR,5) FOR XR = 0.1 0.1 5
PLOT CPSI(XR,2) FOR XR = 0.1 0.1 5
PLOT CPSI(XR,5) FOR XR = 0.1 0.1 5
END OF MULTIPLOT

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