Binomial identities obtained from the Gegenbauer series expansion

DOI10.1080/10652469.2023.2244648OpenAlexW4385753009MaRDI QIDQ6066227

Omran Kouba

Publication date: 15 November 2023

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652469.2023.2244648

zbMATH Keywords

gamma functionGegenbauer polynomialsLegendre polynomialsPochhammer symbolChebyshev polynomials of the first and second kind

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Combinatorial identities, bijective combinatorics (05A19) 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)

Related Items

Applications of a hypergeometric identity and Ramanujan-like series

Cites Work

• On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
• On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions
• Glaisher’s Formulas for $${\frac{1} {{\pi }^{2}}}$$ and Some Generalizations
• Using Fourier-Legendre expansions to derive series for \(\frac{1}{\pi}\) and \(\frac{1}{\pi^{2}}\)
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