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Dataplot Vol 2 Vol 1

I0INT

Name:
    I0INT (LET)
Type:
    Library Function
Purpose:
    This program computes the integral of the modified Bessel function I0(x).
Description:
    The I0INT function is defined as:

      I0INT(x) = {integral 0 to x} I0(t) dt    x >= 0

    with I0 denoting the modified Bessel function of the first kind of order 0.

    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> = I0INT(<x>)             <SUBSET/EXCEPT/FOR qualification>br> where <x> is a non-negative number, variable or parameter;
                <y> is a variable or a parameter (depending on what <x> is) where the computed I0INT function values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = I0INT(2.3)
    PLOT I0INT(X) FOR X = 0 .01 10
    LET X2 = I0INT(X1) FOR X1 = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    BESSI0 = Compute the modified Bessel function of the first kind and order 0.
    BESSI1 = Compute the modified Bessel function of the first kind and order 1.
    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
    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.
    I0ML0 = Compute the difference of the modified Bessel function of the first kind of order 0 and the modified Struve function of order 0.
    I1ML1 = Compute the difference of the modified Bessel function of the first kind of order 1 and the modified Struve function of order 1.
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 I0INT FUNCTION
    PLOT I0INT(X) FOR X = 0 0.01 10
        
    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.