elliptic_integral

elliptic_integral, a Python code which evaluates elliptic integral functions using Carlson's elliptic functions.

The complete and incomplete elliptic integrals of the first, second and third kind can be evaluated, with parameters A (angle in degrees), K (sine of A) or M (the modulus, K^2).

Routines are also supplied to evaluate Jacobi's elliptic functions CN, DN and SN.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

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

Related Data and Programs:

test_values, a Python code which supplies test values of various mathematical functions.

toms577, a Python code which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ. This is a version of ACM TOMS algorithm 577;

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:

• elliptic_integral.py, the source code.
• elliptic_integral.sh, runs all the tests.
• elliptic_integral.txt, the output file.