TOMS577
Carlson's Elliptic Integrals

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

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

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

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.py computes the elementary integral RC(X,Y).
• rd.py computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• rf.py computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• rj.py computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).
• timestamp.py, prints the YMDHMS date as a timestamp.
• toms577_test.py
• toms577_test.txt

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