Precise and fast computation of a general incomplete elliptic integral of third kind by half and double argument transformations

DOI10.1016/J.CAM.2011.11.007zbMath1427.65029OpenAlexW4205096897MaRDI QIDQ2428112

Toshio Fukushima

Publication date: 24 April 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2011.11.007

zbMATH Keywords

Jacobian elliptic functionhalf argument transformationdouble argument transformationLegendre's incomplete elliptic integral

Mathematics Subject Classification ID

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

Related Items (4)

Precise and fast computation of Jacobian elliptic functions by conditional duplication ⋮ Recursive computation of derivatives of elliptic functions and of incomplete elliptic integrals ⋮ Fast computation of a general complete elliptic integral of third kind by half and double argument transformations ⋮ Andoyer's variables and phases in the free rigid body

Uses Software

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• DLMF
• algorithm 577

Cites Work

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• Numerical computation of real or complex elliptic integrals
• Periodic solutions of a derivative nonlinear Schrödinger equation: Elliptic integrals of the third kind
• Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations
• 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
• Precise computation of acceleration due to uniform ring or disk
• Fast computation of incomplete elliptic integral of first kind by half argument transformation
• A certain class of incomplete elliptic integrals and associated definite integrals
• 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
• Precise and fast computation of the general complete elliptic integral of the second kind
• Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
• Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions

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