elliptic_integral


elliptic_integral, a FORTRAN77 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).

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 an Octave version and a Python version.

Related Data and Programs:

elliptic_integral_test

special_functions, a FORTRAN77 library which evaluates special functions, including Airy, Associated Legendre Bessel, Beta, Complete Elliptic Integral, Confluent Hypergeometric, Cosine Integral, Elliptic Integral, Error, Exponential Integral, Fresnel Integral, Gamma, Hankel, Hypergeometric, Incomplete Beta, Incomplete Gamma, Jacobian Elliptic, Kelvin, Lambda, Legendre, Mathieu, Modified Spherical Bessel, Parabolic Cylinder, Psi, Riccati-Bessel, Sine Integral, Spheroidal Wave, Struve, Whittaker, as well as Bernoulli Numbers, Euler Numbers, Hermite Polynomials, Laguerre Polynomials, Legendre Polynomials, by Shanjie Zhang, Jianming Jin;

test_values, a FORTRAN77 library which supplies test values of various mathematical functions.

toms577, a FORTRAN77 library 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:


Last revised on 04 October 2023.