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Dataplot Vol 2 Vol 1

ZETA

Name:
    ZETA (LET)
Type:
    Library Function
Purpose:
    Compute a function of the Riemann Zeta function.
Description:
    The Riemann Zeta function for real s is defined as:

      ZETA(s) = SUM[k=1 to infinity][1/(k**s)]    s > 1

    For better numerical stability, Dataplot actually computes ZETA(s) - 1.

    Dataplot uses a Fortran translation of a C routine given in "Atlas For Computing Mathematical Functions" (see the Reference section below).

Syntax:
    LET <y> = ZETA(<x>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, variable, or parameter (> 1);
                  <y> is a variable or a parameter (depending on what <x> is) where the computed zeta - 1 values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = ZETA(2)
    LET A = ZETA(X)
    LET X2 = ZETA(X) FOR X = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    ETA = Compute the eta function.
    CATLAN = Compute the Catlan Beta function.
    LAMBDA = Compute the lambda function.
Reference:
    "Atlas For Computing Mathematical Functions", William J. Thompson, John wiley & Sons, 1997.

    "AMS 55: Handbook of Mathematical Functions", Abramowitz and Stegun, Eds., Washington, DC, National Bureau of Standards, 1964.

Applications:
    Special Functions
Implementation Date:
    1997/12
Program:
    TITLE AUTOMATIC
    PLOT ZETA(X) FOR X = 1.05 0.01 3

    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.