SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

ATNINT

Name:
    ATNINT (LET)
Type:
    Library Function
Purpose:
    This program computes the integral of the inverse-tangent function.
Description:
    The ATNINT function is defined as:

      ATNINT(x) = integral {0 to x} (arctan t)/t dt

    with arctan denoting the inverse tangent function.

    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> = ATNINT(<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 ATNINT function values are stored;
    and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
    LET A = ATNINT(2.3)
    PLOT ATNINT(X) FOR X = 0 0.01 5
    LET X2 = ATNINT(X1) FOR X1 = 0.1 0.1 3.0
Default:
    None
Synonyms:
    None
Related Commands:
    TAN = Compute the tangent function.
    ARCTAN = Compute the arctangent (=inverse) function.
    ARCTANH = Compute the hyperbolic arctangent function.
    LOGINT = Compute the logarithmic integral.
    EXPINTN = Compute the exponential integral of order N.
    SININT = Compute the sine integral.
    COSINT = Compute the cosine integral.
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 INVERSE-TANGENT (ATNINT) FUNCTION
    PLOT ATNINT(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.