A q-analogue of a curious supercongruence of Guillera and Zudilin

DOI10.1080/10236198.2019.1572129zbMath1411.11021OpenAlexW2913326345MaRDI QIDQ4632381

Victor J. W. Guo

Publication date: 29 April 2019

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

Full work available at URL: https://doi.org/10.1080/10236198.2019.1572129

zbMATH Keywords

cyclotomic polynomialsWilf-Zeilberger method$q$-binomial coefficients$q$-WZ pair

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) (q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Congruences for modular and (p)-adic modular forms (11F33) Numerical methods for difference and functional equations, recurrence relations (65Q99)

Related Items (10)

On a \(q\)-deformation of modular forms ⋮ Factors of some truncated basic hypergeometric series ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ Some congruences related to a congruence of Van Hamme ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series: even powers ⋮ A -ANALOGUE OF A HYPERGEOMETRIC CONGRUENCE ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial ⋮ \(q\)-analogues of two ``divergent Ramanujan-type supercongruences

Cites Work

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• Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers
• The \(q\)-Markov-WZ method
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• A q-Analogue of Wolstenholme's Harmonic Series Congruence

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