ELLIPTIC_INTEGRAL
Elliptic Integrals

ELLIPTIC_INTEGRAL, a FORTRAN77 library 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).

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:

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:

• elliptic_integral.f, the source code.

Examples and Tests:

• elliptic_integral_test.f, a sample calling program.
• elliptic_integral_test.txt, the output file.

List of Routines:

• ELLIPTIC_EA evaluates the complete elliptic integral E(A).
• ELLIPTIC_EA_VALUES: values of the complete elliptic integral E(ALPHA).
• ELLIPTIC_EK evaluates the complete elliptic integral E(K).
• ELLIPTIC_EK_VALUES returns values of the complete elliptic integral E(K).
• ELLIPTIC_EM evaluates the complete elliptic integral E(M).
• ELLIPTIC_EM_VALUES returns values of the complete elliptic integral E(M).
• ELLIPTIC_FA evaluates the complete elliptic integral F(A).
• ELLIPTIC_FA_VALUES: values of the complete elliptic integral F(ALPHA).
• ELLIPTIC_FK evaluates the complete elliptic integral F(K).
• ELLIPTIC_FK_VALUES returns values of the complete elliptic integral F(K).
• ELLIPTIC_FM evaluates the complete elliptic integral F(M).
• ELLIPTIC_FM_VALUES returns values of the complete elliptic integral F(M).
• ELLIPTIC_PIA evaluates the complete elliptic integral Pi(N,A).
• ELLIPTIC_PIA_VALUES returns values of the complete elliptic integral Pi(N,A).
• ELLIPTIC_PIK evaluates the complete elliptic integral Pi(N,K).
• ELLIPTIC_PIK_VALUES returns values of the complete elliptic integral Pi(N,K).
• ELLIPTIC_PIM evaluates the complete elliptic integral Pi(N,M).
• ELLIPTIC_PIM_VALUES returns values of the complete elliptic integral Pi(N,M).
• 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).
• TIMESTAMP prints out the current YMDHMS date as a timestamp.

You can go up one level to the FORTRAN77 source codes.