toms577


toms577, a FORTRAN90 code which evaluates Carlson's elliptic integral functions RC, RD, RF and RJ.

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

Licensing:

The computer code and data files made available on this web page are distributed under the MIT 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 FORTRAN90 code which evaluates complete elliptic integrals of first, second and third kind, using Carlson's elliptic integral functions.

SPECIAL_FUNCTIONS, a FORTRAN90 code 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 FORTRAN90 code 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:


Last revised on 13 March 2021.