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Dataplot Vol 2 Vol 1

BIRINT

Name:
    BIRINT (LET)
Type:
    Library Function
Purpose:
    This program computes the integral of the Airy function Bi(x).
Description:
    The BIRINT function is defined as:

      BIRINT(x) = {integral 0 to x} Bi(t) dt

    with Bi denoting the Airy function of the second kind.

    Dataplot computes this function using ACM Algorithm 757 (see Reference: below). The function is computed using Chebyshev expansions, the coefficients of which are given to 20 decimal places.

Syntax:
    LET <y> = BIRINT(<x>)             <SUBSET/EXCEPT/FOR qualification>
    where <x> is a number, variable or parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed BIRINT function values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = BIRINT(2.3)
    PLOT BIRINT(X) FOR X = -5 0.01 5
    LET X2 = BIRINT(X1) FOR X1 = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    BAIRY = Compute the Airy function of the second kind.
    AIRY = Compute the Airy function.
    AIRINT = Compute the integral of the Airy function.
    BESSIN = Compute the modified Bessel function of the first kind and order N.
    BESSJN = Compute the Bessel function of the first kind and order N.
    BESSKN = Compute the modified Bessel function of the third kind and order N.
    BESSYN = Compute the Bessel function of the second kind and order N.
    J0INT = Compute the integral of the Bessel function of the first kind and order 0.
    K0INT = Compute the integral of the modified Bessel function of the third kind and order 0.
    Y0INT = Compute the integral of the Bessel function of the second kind and order 0.
Reference:
    "ACM Transactions of Mathematical Software", Allan MacLead, Vol. 22, No. 3, September, 1996, pp. 288-301.
Applications:
    Special Functions
Implementation Date:
    2005/11
Program:
    TITLE BIRINT FUNCTION
    PLOT BIRINT(X) FOR X = -5 0.01 5
        
    plot generated by sample program

Date created: 11/7/2005
Last updated: 11/7/2005
Please email comments on this WWW page to alan.heckert@nist.gov.