Factors of some truncated basic hypergeometric series

DOI10.1016/j.jmaa.2019.04.021zbMath1448.33016arXiv1901.07908OpenAlexW2912272050WikidataQ128117047 ScholiaQ128117047MaRDI QIDQ2633884

Victor J. W. Guo

Publication date: 10 May 2019

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

Full work available at URL: https://arxiv.org/abs/1901.07908

zbMATH Keywords

cyclotomic polynomialsbasic hypergeometric series\(q\)-binomial theoremsupercongruence

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Congruences; primitive roots; residue systems (11A07) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (15)

Some \(q\)-supercongruences from Gasper's Karlsson-Minton type summation ⋮ Factors of certain basic hypergeometric sums ⋮ Divisibility results concerning truncated hypergeometric series ⋮ A family of \(q\)-hypergeometric congruences modulo the fourth power of a cyclotomic polynomial ⋮ On the divisibility of some truncated hypergeometric series ⋮ Congruences for the truncated Appell series F₃ and F₄ ⋮ $q$-Supercongruences from the $q$-Saalschütz identity ⋮ Some congruences related to a congruence of Van Hamme ⋮ A -ANALOGUE OF A HYPERGEOMETRIC CONGRUENCE ⋮ Some new \(q\)-congruences for truncated basic hypergeometric series ⋮ Common \(q\)-analogues of some different supercongruences ⋮ Some $q$-congruences with parameters ⋮ Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial ⋮ Some symmetric \(q\)-congruences modulo the square of a cyclotomic polynomial ⋮ Further \(q\)-supercongruences from the \(q\)-Pfaff-Saalschütz identity

Cites Work

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• On sums of Apéry polynomials and related congruences
• Supercongruences motivated by \(e\)
• The Rodriguez-Villegas type congruences for truncated \(q\)-hypergeometric functions
• A supercongruence motivated by the Legendre family of elliptic curves
• Some \(q\)-analogues of supercongruences of Rodriguez-Villegas
• Ramanujan-type supercongruences
• A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
• Factors of sums and alternating sums of products of \(q\)-binomial coefficients and powers of \(q\)-integers
• A \(q\)-microscope for supercongruences
• A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
• Super congruences and Euler numbers
• Some new \(q\)-congruences for truncated basic hypergeometric series
• \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
• On a \(q\)-deformation of modular forms
• Supercongruences for a truncated hypergeometric series
• Congruences concerning Legendre polynomials
• On a conjectured q-congruence of Guo and Zeng
• A q-analogue of the (I.2) supercongruence of Van Hamme
• Proof of a q-congruence conjectured by Tauraso
• A q-analogue of a curious supercongruence of Guillera and Zudilin
• Some $q$-congruences with parameters
• Proof of a basic hypergeometric supercongruence modulo the fifth power of a cyclotomic polynomial

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