TOMS577
Carlson's Elliptic Integrals

TOMS577, a MATLAB library which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ.

The text of many ACM TOMS algorithms is available online through ACM: http://calgo.acm.org/ or NETLIB: http://www.netlib.org/toms/index.html.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

TOMS577 is available in a C++ version and a C version and a FORTRAN77 version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

ELLIPTIC_INTEGRAL, a MATLAB library which evaluates complete elliptic integrals of first, second and third kind, using Carlson's elliptic integral functions.

TEST_VALUES, a MATLAB library which supplies test values of various mathematical functions.

toms577_test

Reference:

1. Bille Carlson,
   Computing Elliptic Integrals by Duplication,
   Numerische Mathematik,
   Volume 33, 1979, pages 1-16.
2. Bille Carlson, Elaine Notis,
   Algorithm 577, Algorithms for Incomplete Elliptic Integrals,
   ACM Transactions on Mathematical Software,
   Volume 7, Number 3, pages 398-403, September 1981.

Source Code:

• rc.m computes the elementary integral RC(X,Y).
• rd.m computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• rf.m computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• rj.m computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
• timestamp.m, prints the YMDHMS date as a timestamp.