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Dataplot Vol 2 Vol 1

ETA

Name:
    ETA (LET)
Type:
    Library Function
Purpose:
    Compute the eta function.
Description:
    The eta function is defined as:

      ETA(s) = SUM((-1)**(k-1)/(k**s), s >= 1 and the summation is for k = 1 to infinity

    For better numerical stability, Dataplot actually computes ETA(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> = ETA(<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 eta - 1 values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = ETA(2)
    LET A = ETA(X)
    LET X2 = ETA(X) FOR X = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    ZETA = Compute the Riemann Zeta 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, pp. 144-151.
Applications:
    Special Functions
Implementation Date:
    1997/12
Program:
    TITLE AUTOMATIC
    PLOT ETA(X) FOR X = 1.01 0.01 5

    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.