Polynomial reduction and supercongruences

DOI10.1016/j.jsc.2019.11.004OpenAlexW2989664298MaRDI QIDQ2211192

Yan-Ping Mu, Doron Zeilberger, Qing-Hu Hou

Publication date: 13 November 2020

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.09391

zbMATH Keywords

polynomial reductionsupercongruencehypergeometric term

Mathematics Subject Classification ID

Congruences; primitive roots; residue systems (11A07) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (8)

Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Polynomial reduction for holonomic sequences and applications in \(\pi\)-series and congruences ⋮ Supercongruences for sums involving fourth power of some rising factorials ⋮ Proof of a generalization of the (C.2) supercongruence of Van Hamme ⋮ PROOF OF TWO CONJECTURES ON SUPERCONGRUENCES INVOLVING CENTRAL BINOMIAL COEFFICIENTS ⋮ Factors of certain sums involving central \(q\)-binomial coefficients ⋮ \(q\)-rational reduction and \(q\)-analogues of series for \(\pi\) ⋮ Gosper summability of rational multiples of hypergeometric terms

Cites Work

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• On the supercongruence conjectures of van Hamme
• The extended Zeilberger algorithm with parameters
• Hypergeometric evaluation identities and supercongruences
• Rational normal forms and minimal decompositions of hypergeometric terms
• Ramanujan-type supercongruences
• Semi-automated proof of supercongruences on partial sums of hypergeometric series
• Rational summation and Gosper-Petkovšek representation
• Common \(q\)-analogues of some different supercongruences
• A refinement of a congruence result by van Hamme and Mortenson
• Supercongruences involving products of two binomial coefficients
• Supercongruences for sporadic sequences
• A Modified Abramov-Petkovsek Reduction and Creative Telescoping for Hypergeometric Terms
• Minimal decomposition of indefinite hypergeometric sums
• Gaussian Hypergeometric series and supercongruences
• A $p$-adic supercongruence conjecture of van Hamme
• Some generalizations of a supercongruence of van Hamme
• Some supercongruences involving
• A Gaussian hypergeometric series evaluation and Apéry number congruences
• Supercongruences for sums involving rising factorial
• On Sums Related to Central Binomial and Trinomial Coefficients

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