Some supercongruences on truncated hypergeometric series

DOI10.1080/10236198.2017.1418863zbMath1435.11009arXiv1610.03799OpenAlexW3207649846MaRDI QIDQ5243407

Ji-Cai Liu

Publication date: 18 November 2019

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.03799

zbMATH Keywords

supercongruencestruncated hypergeometric series\(p\)-adic gamma functions

Mathematics Subject Classification ID

Other analytic theory (analogues of beta and gamma functions, (p)-adic integration, etc.) (11S80) Congruences; primitive roots; residue systems (11A07) Generalized hypergeometric series, ({}_pF_q) (33C20) Special functions in characteristic (p) (gamma functions, etc.) (33E50)

Related Items (9)

Some \(q\)-analogues of supercongruences for truncated \({}_3 F_2\) hypergeometric series ⋮ Some q-supercongruences related to Swisher’s (H.3) conjecture ⋮ A common \(q\)-analogue of two supercongruences ⋮ Proof of some conjectural hypergeometric supercongruences via curious identities ⋮ Congruences corresponding to hypergeometric identities. I: \(_2F_1\) transformations ⋮ A new \(q\)-extension of the (H.2) congruence of Van Hamme for primes \(p\equiv 1\pmod{4}\) ⋮ Another family of \(q\)-congruences modulo the square of a cyclotomic polynomial ⋮ A family of \(q\)-congruences modulo the square of a cyclotomic polynomial ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)

Uses Software

• SIGMA

Cites Work

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