A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula

DOI10.1016/j.jcta.2022.105705zbMath1506.11007OpenAlexW4307488654MaRDI QIDQ2102699

Chuanan Wei

Publication date: 29 November 2022

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2022.105705

zbMATH Keywords

summation formulasBernoulli numberscyclotomic polynomialsbasic hypergeometric seriesChinese remainder theoremharmonic numberscreative microscoping method\(q\)-supercongruences

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Polynomials in number theory (11C08) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20)

Related Items (7)

Three families of \(q\)-supercongruences from a quadratic transformation of Rahman ⋮ Some \(q\)-supercongruences related to Van Hamme's (C.2) supercongruence ⋮ A new extension of Van Hamme's (E.2) supercongruence ⋮ Generalizations of the (F.2) supercongruence of Van Hamme ⋮ A new \(q\)-variation of the (C.2) supercongruence of Van Hamme ⋮ A new extension of a “divergent” Ramanujan-type supercongruence ⋮ Factors of certain basic hypergeometric sums

Cites Work

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