Some congruences involving powers of Legendre polynomials

DOI10.1080/10652469.2015.1034123zbMath1360.11007OpenAlexW2074422329MaRDI QIDQ5262280

Victor J. W. Guo

Publication date: 13 July 2015

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

Full work available at URL: https://doi.org/10.1080/10652469.2015.1034123

zbMATH Keywords

congruencesLegendre polynomialsZeilberger's algorithmFermat's little theoremClausen's formula

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Congruences; primitive roots; residue systems (11A07)

Related Items (9)

A supercongruence involving Delannoy numbers and Schröder numbers ⋮ Some congruences on Delannoy numbers and Schröder numbers ⋮ Proof of some divisibility results on sums involving binomial coefficients ⋮ Some parametric congruences involving generalized central trinomial coefficients ⋮ Congruences involving squares of generalized central trinomial coefficients ⋮ Proof of two congruences concerning Legendre polynomials ⋮ On the divisibility of sums involving powers of multi-variable Schmidt polynomials ⋮ ON THE DIVISIBILITY OF SUMS INVOLVING APÉRY-LIKE POLYNOMIALS ⋮ Proof of Sun’s conjectures on Schröder-like numbers

Cites Work

• Proof of some conjectures of Z.-W. Sun on congruences for Apéry polynomials
• On sums of Apéry polynomials and related congruences
• Congruences involving generalized central trinomial coefficients
• On Delannoy numbers and Schröder numbers
• On divisibility of sums of Apéry polynomials
• New congruences for central binomial coefficients
• Congruences concerning Legendre polynomials. II
• A note on lattice chains and Delannoy numbers
• Supercongruences for the Catalan-Larcombe-French numbers

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