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Dataplot Vol 2 Vol 1


    Library Function
    Compute the hypergeometric function with shape parameters A, B, and C for the convergent case (case where x < 1).
    The integral representation of the hypergeomtric function is

      formula for hypergeometric function

    This function only tries to compute the hypergeometric function for the convergent case, which is ABS(x) < 1 and C <= A + b.

    Although many common functions can be defined as a special case of this function, it is typically better to use functions that take advantage of features of the specific function for more efficient and accurate evaluation.

    The input value must be have an absolute value less than 1. The C shape parameter should not be 0 or a negative integer. Also, if C <= A + B, the hypergeometric function is divergent and Dataplot will not attempt to conpute the function for this case either.

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

    LET <y> = HYPERGEO(<x>,<a>,<b>,<c>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, variable, or parameter;
                <a> is a number, variable, or parameter;
                <b> is a number, variable, or parameter;
                <b> is a number, variable, or parameter;
                <c> is a number, variable, or parameter;
                <y> is a variable or a parameter (depending on what <a>, <b>, and <c> are) where the computed values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
    LET Z = HYPERGEO(0.01,0.1,0.2,2)
    LET Z = HYPERGEO(1,0.1,0.2,2)
    LET Z = HYPERGEO(0.1,-1.3,0.1,4)
Related Commands:
    CHU = Compute the confluent hypergeometric U function.
    CHM = Compute the confluent hypergeometric M function.
    BETA = Compute the complete Beta function.
    BETAI = Compute the incomplete Beta function.
    GAMMA = Compute the gamma function.
    LOGGAMMA = Compute the log gamma function.
    "Computation of Special Functions", Shanjie Zhang and Jianming Jin, John Wiley and Sons, 1996, chapter 12.

    "Handbook of Mathematical Functions, Applied Mathematics Series, Vol. 55", Abramowitz and Stegun, National Bureau of Standards, 1964.

    Special Functions
Implementation Date:
    PLOT HYPERGEO(X,1,2,4) FOR X = -0.9 0.01 0.9

    plot generated by sample program

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