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Dataplot Vol 2 Vol 1

LAMBDAP

Name:
    LAMBDAP (LET)
Type:
    Library Function
Purpose:
    Compute the derivative of the lambda function.
Description:
    The lambda function is defined as:

      f(x,v) = 2**V*GAMMA(v+1)*[J(x,v)/x**v)  (v <> -1, -2, ...)

    where v is the order of the lambda function, GAMMA is the gamma function, and J(x,v) is the Bessel function of the first kind. Dataplot supports a maximum order of 500.

    The derivative of the lambda function can be defined in terms of the lambda function:

      f'(x,v) = (2*v/x)[f(x,v-1) - f(x,v)]

    Dataplot computes this function using the LAMV and LAMN routines from "Computation of Special Functions" (see the Reference section below).

Syntax:
    LET <y> = LAMBDAP(<x>,<v>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, variable or parameter;
                <v> is a number, parameter, or variable (less than 500);
                <y> is a variable or a parameter (depending on what <x> and <v> are) where the computed lambda function derivative values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = LAMBDAP(2.3,1)
    LET A = LAMBDAP(X,A1)
    LET X2 = LAMBDAP(X1,4) FOR X1 = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    LAMBDA = Compute the lambda function.
    GAMMA = Compute the gamma function.
    BESSJN = Compute the Bessel function of the first kind.
Reference:
    "Computation of Special Functions", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, pp. 182-184.
Applications:
    Special Functions
Implementation Date:
    1997/12
Program:
    MULTIPLOT 2 2
    MULTIPLOT CORNER COORDINATES 5 5 95 95
    TITLE ORDER 0
    PLOT LAMBDAP(X,0) FOR X = 0 0.01 10
    TITLE ORDER 1
    PLOT LAMBDAP(X,1) FOR X = 0 0.01 10
    TITLE ORDER 2
    PLOT LAMBDAP(X,2) FOR X = 0 0.01 10
    TITLE ORDER 3
    PLOT LAMBDAP(X,3) FOR X = 0 0.01 10
    END OF MULTIPLOT
    MOVE 50 97
    JUSTIFICATION CENTER
    TEXT DERIVATIVE OF LAMBDA FUNCTIONS

    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.