Some congruences that extend Van Hamme's (D.2) supercongruence

DOI10.1016/j.jmaa.2023.127344MaRDI QIDQ6110853

Haihong He, Xiaoxia Wang

Publication date: 6 July 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Chinese remainder theoremsupercongruencecreative microscoping\(q\)-supercongruenceWatson's \(_8\phi_7\) transformationJackon's \(_8\phi_7\) summation

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (6)

Some new results about 𝑞-trinomial coefficients ⋮ A new extension of Van Hamme's (E.2) supercongruence ⋮ Some \(q\)-supercongruences from squares of basic hypergeometric series ⋮ A new \(q\)-variation of the (C.2) supercongruence of Van Hamme ⋮ Some new \(q\)-supercongruences involving one free parameter ⋮ A new extension of a “divergent” Ramanujan-type supercongruence

Cites Work

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• Some supercongruences occurring in truncated hypergeometric series
• A \(q\)-microscope for supercongruences
• Some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial
• Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme
• \(q\)-supercongruences on triple and quadruple sums
• A new extension of the (A.2) supercongruence of Van Hamme
• \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping
• A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial
• \(q\)-supercongruences from gasper and Rahman's summation formula
• Proofs of Guo and Schlosser's two conjectures
• An extension of a supercongruence of Long and Ramakrishna
• A NEW -ANALOGUE OF VAN HAMME’S (A.2) SUPERCONGRUENCE
• NEW GENERALISATIONS OF VAN HAMME’S (G.2) SUPERCONGRUENCE
• A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES

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