Expansions over Legendre polynomials and infinite double series identities

DOI10.1007/s11139-022-00663-4OpenAlexW4313334755MaRDI QIDQ2688343

John Maxwell Campbell, Chu, Wenchang

Publication date: 2 March 2023

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-022-00663-4

zbMATH Keywords

gamma functionhypergeometric seriesproduct integrationLegendre polynomialFourier-Legendre seriesmultinomial coefficientcentral binomial coefficient

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical summation of series (65B10)

Related Items (2)

New Clebsch–Gordan‐type integrals involving threefold products of complete elliptic integrals ⋮ On a higher-order version of a formula due to Ramanujan

Cites Work

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• Transformation and summation formulas for Kampé de Fériet series \(F^{0:3}_{1:1} (1,1)\)
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• A transformation formula for double hypergeometric series
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• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials
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• New families of double hypergeometric series for constants involving ${1}/{\pi ^2}$
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• Elliptic Integrals in Terms of Legendre Polynomials

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