Numerical computation of inverse complete elliptic integrals of first and second kinds

DOI10.1016/j.cam.2013.02.003zbMath1302.65060OpenAlexW2006996544MaRDI QIDQ2448309

Toshio Fukushima

Publication date: 30 April 2014

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.2013.02.003

zbMATH Keywords

inversioncomplete elliptic integral

Mathematics Subject Classification ID

Computation of special functions and constants, construction of tables (65D20) Numerical integration (65D30) Elliptic functions and integrals (33E05) Numerical approximation and evaluation of special functions (33F05)

Related Items (4)

Large-spin expansions of GKP strings ⋮ 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 ⋮ Fast switch and spline scheme for accurate inversion of nonlinear functions: the new first choice solution to Kepler's equation

Uses Software

• Mathematica
• DLMF
• algorithm 577
• LambertW

Cites Work

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• Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
• Chebyshev Polynomial Expansions of Complete Elliptic Integrals
• Numerical evaluation of the Lambert W function and application to generation of generalized Gaussian noise with exponent 1/2
• Numerical Methods for Special Functions
• Chebyshev Approximations for the Complete Elliptic Integrals K and E

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