TOMS577
Carlson's Elliptic Integrals

TOMS577, a FORTRAN90 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 FORTRAN90 library which evaluates complete elliptic integrals of first, second and third kind, using Carlson's elliptic integral functions.

SPECIAL_FUNCTIONS, a FORTRAN90 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 FORTRAN90 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:

• toms577.f90, the source code.

Examples and Tests:

• toms577_test.f90, a sample calling program.
• toms577_test.txt, the output file.

List of Routines:

• RC computes the elementary integral RC(X,Y).
• RD computes an incomplete elliptic integral of the second kind, RD(X,Y,Z).
• RF computes an incomplete elliptic integral of the first kind, RF(X,Y,Z).
• RJ computes an incomplete elliptic integral of the third kind, RJ(X,Y,Z,P).

You can go up one level to the FORTRAN90 source codes.