Legendre polynomials and Ramanujan-type series for \(1/\pi\)

DOI10.1007/s11856-012-0081-5zbMath1357.11123OpenAlexW2043220612MaRDI QIDQ1955736

Heng Huat Chan, Wadim Zudilin, James G. Wan

Publication date: 18 June 2013

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

Full work available at URL: https://doi.org/10.1007/s11856-012-0081-5

zbMATH Keywords

identitiesgenerating functionLegendre polynomialsRamanujan-type seriesproduct of two Gaussian hypergeometric functions

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Theta series; Weil representation; theta correspondences (11F27) Evaluation of number-theoretic constants (11Y60)

Related Items (18)

Generating functions of Legendre polynomials: a tribute to Fred Brafman ⋮ Complex series for \(1/\pi\) ⋮ The Bailey-Brafman identity and its analogues ⋮ Some new series for $1/\pi $ motivated by congruences ⋮ New series for powers of \(\pi\) and related congruences ⋮ On two congruences involving Franel numbers ⋮ Short Walk Adventures ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Congruences on truncated double summation series ⋮ Generating functions of Legendre polynomials: A tribute to Fred Brafman ⋮ On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions ⋮ A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\frac{520}{\pi}$ ⋮ A generalization of a Brafman-Bailey type identity ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms ⋮ Proof of a rational Ramanujan-type series for 1/π. The fastest one in level 3 ⋮ Series for 1/π using Legendre's relation ⋮ Ramanujan-type supercongruences involving Almkvist-Zudilin numbers

Cites Work

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• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• Some arithmetic properties of short random walk integrals
• Generating functions of Legendre polynomials: A tribute to Fred Brafman
• “Divergent” Ramanujan-type supercongruences
• Inversion formulas for elliptic functions
• Ramanujan's Theories of Elliptic Functions to Alternative Bases
• Generating Functions of Jacobi and Related Polynomials
• On Ramanujan's quartic theory of elliptic functions
• Eisenstein series and approximations to \(\pi\)

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