A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS

DOI10.1017/S0004972713000233zbMath1334.33022arXiv1210.2493MaRDI QIDQ5406100

Wadim Zudilin

Publication date: 1 April 2014

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2493

zbMATH Keywords

Legendre polynomialmodular functiongenerating series\(\pi\)binomial sum

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Modular and automorphic functions (11F03) Holomorphic modular forms of integral weight (11F11) Generalized hypergeometric series, ({}_pF_q) (33C20) Evaluation of number-theoretic constants (11Y60)

Related Items (5)

New series for powers of \(\pi\) and related congruences ⋮ Equilibration properties of small quantum systems: further examples ⋮ A modular supercongruence for _6F_5: An Apéry-like story ⋮ Short Walk Adventures ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms

Cites Work

• Unnamed Item
• New analogues of Clausen's identities arising from the theory of modular forms
• Generating functions of Legendre polynomials: A tribute to Fred Brafman
• Sporadic sequences, modular forms and new series for \(1/\pi\)
• Eisenstein series and theta functions to the septic base
• Rational analogues of Ramanujan's series for 1/π
• NEW REPRESENTATIONS FOR APÉRY‐LIKE SEQUENCES
• The Generating Function of Jacobi Polynomials

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