elliptic_integral


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

The complete and incomplete elliptic functions 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).

The Jacobi elliptic functions CN(U,M), DN(U,M) and SN(U,M) can be evaluated with parameter M.

Licensing:

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

Languages:

elliptic_integral 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:

elfun, a MATLAB code which evaluates elliptic integrals and Jacobi elliptic functions cn(), dn(), sn(), by Milan Batista.

elliptic_integral_test

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

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

Reference:

  1. Roland Bulirsch,,
    Numerical calculation of elliptic integrals and elliptic functions,,
    Numerische Mathematik,,
    Volume 7, Number 1, 1965, pages 78-90.
  2. Bille Carlson,
    Computing Elliptic Integrals by Duplication,
    Numerische Mathematik,
    Volume 33, 1979, pages 1-16.
  3. 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:


Last revised on 19 November 2020.