Four ways to compute the inverse of the complete elliptic integral of the first kind

DOI10.1016/j.cpc.2015.05.006zbMath1360.65080OpenAlexW246163639MaRDI QIDQ525638

John P. Boyd

Publication date: 5 May 2017

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cpc.2015.05.006

zbMATH Keywords

Chebyshev polynomialselliptic integralpseudospectralinverse elliptic integral

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 (1)

Fast switch and spline scheme for accurate inversion of nonlinear functions: the new first choice solution to Kepler's equation

Uses Software

• Matlab
• DLMF
• Equator

Cites Work

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• Numerical computation of real or complex elliptic integrals
• Numerical, perturbative and Chebyshev inversion of the incomplete elliptic integral of the second kind
• Numerical inversion of a general incomplete elliptic integral
• Precise and fast computation of a general incomplete elliptic integral of second kind by half and double argument transformations
• Computing elliptic integrals by duplication
• Orthogonal rational functions on a semi-infinite interval
• Numerical calculation of elliptic integrals and elliptic functions.II
• Numerical calculation of elliptic integrals and elliptic functions
• Numerical computation of inverse complete elliptic integrals of first and second kinds
• Finding the Zeros of a Univariate Equation: Proxy Rootfinders, Chebyshev Interpolation, and the Companion Matrix
• Solving Transcendental Equations
• Precise and fast computation of the general complete elliptic integral of the second kind
• Algorithm 577: Algorithms for Incomplete Elliptic Integrals [S21]
• Inversion of the perturbation series
• Chebyshev Approximations for the Complete Elliptic Integrals K and E
• On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds
• Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kinds
• New Formulas for Computing Incomplete Elliptic Integrals of the First and Second Kind

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