On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions

DOI10.1016/j.jmaa.2019.06.017zbMath1423.33003arXiv1710.03221OpenAlexW2950705685WikidataQ127775177 ScholiaQ127775177MaRDI QIDQ2320074

Jacopo D'Aurizio, John Maxwell Campbell, Jonathan Sondow

Publication date: 21 August 2019

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.03221

zbMATH Keywords

infinite serieshypergeometric seriescomplete elliptic integralharmonic numberFourier-Legendre theory

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Elliptic functions and integrals (33E05) Higher logarithm functions (33B30)

Related Items (26)

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Cites Work

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• Legendre functions, spherical rotations, and multiple elliptic integrals
• Moments of products of elliptic integrals
• Ramanujan-like series for \(\frac{1}{\pi}\) involving harmonic numbers
• Generating functions of Legendre polynomials: A tribute to Fred Brafman
• Legendre polynomials and Ramanujan-type series for \(1/\pi\)
• Surprising identities for the hypergeometric \({}_{4}F_{3}\) function
• Series containing squared central binomial coefficients and alternating harmonic numbers
• Combinatorial and hypergeometric identities via the Legendre polynomials -- a computational approach
• Series for 1/π using Legendre's relation
• Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals
• Legendre-type relations for generalized complete elliptic integrals
• An integral transform related to series involving alternating harmonic numbers
• Hypergeometry of the Parbelos
• Legendre Polynomial Expansions of Hypergeometric Functions with Applications
• Generating Functions of Jacobi and Related Polynomials
• Elliptic Integrals in Terms of Legendre Polynomials
• Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)

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