Precise and fast computation of the general complete elliptic integral of the second kind

DOI10.1090/S0025-5718-2011-02455-5zbMath1223.33038MaRDI QIDQ3015054

Toshio Fukushima

Publication date: 8 July 2011

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

relative errorelliptic integral\texttt{Mathematica}Taylor coefficient\texttt{ce12}

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Elliptic functions and integrals (33E05) Numerical approximation and evaluation of special functions (33F05)

Related Items (9)

Precise and fast computation of a general incomplete elliptic integral of third kind by half and double argument transformations ⋮ Precise and fast computation of Jacobian elliptic functions by conditional duplication ⋮ Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals ⋮ Generalized Hersch-Pfluger distortion function and complete elliptic integrals ⋮ Numerical computation of inverse complete elliptic integrals of first and second kinds ⋮ Fast computation of a general complete elliptic integral of third kind by half and double argument transformations ⋮ Four ways to compute the inverse of the complete elliptic integral of the first kind ⋮ Precise and fast computation of complete elliptic integrals by piecewise minimax rational function approximation ⋮ Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations

Uses Software

• Mathematica
• algorithm 577

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fast computation of Jacobian elliptic functions and incomplete elliptic integrals for constant values of elliptic parameter and elliptic characteristic
• Fast computation of complete elliptic integrals and Jacobian elliptic functions
• Fast computation of incomplete elliptic integral of first kind by half argument transformation
• Computing elliptic integrals by duplication
• Numerical computation of incomplete elliptic integrals of a general form
• Numerical calculation of elliptic integrals and elliptic functions.II
• Numerical calculation of elliptic integrals and elliptic functions
• An extension of the Bartky-transformation to incomplete elliptic integrals of the third kind
• Numerical calculation of elliptic integrals and elliptic functions. III
• Chebyshev Polynomial Expansions of Complete Elliptic Integrals
• Chebyshev Approximations for the Complete Elliptic Integrals K and E

This page was built for publication: Precise and fast computation of the general complete elliptic integral of the second kind