Generating functions of Legendre polynomials: A tribute to Fred Brafman

DOI10.1016/j.jat.2011.12.001zbMath1242.33018OpenAlexW2964181825MaRDI QIDQ765820

Wadim Zudilin, James G. Wan

Publication date: 22 March 2012

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2011.12.001

zbMATH Keywords

hypergeometric seriesLegendre polynomialmodular functionBrafman's generating functionClausen's identityApéry-like sequenceseries for \(\pi \)

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Generalized hypergeometric series, ({}_pF_q) (33C20) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (12)

The Bailey-Brafman identity and its analogues ⋮ Implementation of an accurate method for the analysis and simulation of electrical R‐L circuits ⋮ New series for powers of \(\pi\) and related congruences ⋮ Legendre polynomials and Ramanujan-type series for \(1/\pi\) ⋮ Short Walk Adventures ⋮ A GENERATING FUNCTION OF THE SQUARES OF LEGENDRE POLYNOMIALS ⋮ Unnamed Item ⋮ On the interplay among hypergeometric functions, complete elliptic integrals, and Fourier-Legendre expansions ⋮ A SOLUTION OF SUN'S $520 CHALLENGE CONCERNING $\frac{520}{\pi}$ ⋮ Ramanujan-type \(1/\pi\)-series from bimodular forms ⋮ Generalizations and specializations of generating functions for Jacobi, Gegenbauer, Chebyshev and Legendre polynomials with definite integrals ⋮ Series for 1/π using Legendre's relation

Cites Work

• Unnamed Item
• Eisenstein series and Ramanujan-type series for \(1 / \pi\)
• New analogues of Clausen's identities arising from the theory of modular forms
• Legendre polynomials and Ramanujan-type series for \(1/\pi\)
• Generalizations of Clausen's Formula and algebraic transformations of Calabi–Yau differential equations
• Rational analogues of Ramanujan's series for 1/π
• GENERATING FUNCTIONS AND ASSOCIATED LEGENDRE POLYNOMIALS
• An Equivalence Theorem on Generating Functions
• Generating Functions of Jacobi and Related Polynomials

This page was built for publication: Generating functions of Legendre polynomials: A tribute to Fred Brafman