Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity

DOI10.1090/mcom/3874zbMath1525.33012arXiv2208.05242MaRDI QIDQ6133446

Unnamed Author, Dmitriĭ Borisovich Karp

Publication date: 18 August 2023

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

Full work available at URL: https://arxiv.org/abs/2208.05242

zbMATH Keywords

Legendre's elliptic integralsincomplete elliptic integral of the second kind

Mathematics Subject Classification ID

Generalized hypergeometric series, ({}_pF_q) (33C20) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60) Elliptic functions and integrals (33E05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• Inequalities and monotonicity of ratios for generalized hypergeometric function
• Computing elliptic integrals by duplication
• The method of creative telescoping
• Analytic continuation of the Appell function \(F_1\) and integration of the associated system of equations in the logarithmic case
• NIST digital library of mathematical functions
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Asymptotic approximations for the first incomplete elliptic integral near logarithmic singularity
• An approximation for zero-balanced Appell function \(F_{1}\) near (1,1)
• Asymptotic Expansion of the First Elliptic Integral
• Asymptotic Approximations for Symmetric Elliptic Integrals
• Asymptotic expansions and inequalities for hypergeometric function
• Asymptotic Expansions of Symmetric Standard Elliptic Integrals
• On the Series Expansion Method for Computing Incomplete Elliptic Integrals of the First and Second Kinds
• Some Series and Bounds for Incomplete Elliptic Integrals
• Auxiliary Table for the Incomplete Elliptic Integrals
• Uniform asymptotic expansions of symmetric elliptic integrals

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