Two curious \(q\)-supercongruences and their extensions
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Publication:6612607
DOI10.1515/forum-2023-0164MaRDI QIDQ6612607
Publication date: 1 October 2024
Published in: Forum Mathematicum (Search for Journal in Brave)
congruence\(q\)-binomial theoremcyclotomic polynomialcreative microscoping\(q\)-supercongruenceKarlsson-Minton-type summation
(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences; primitive roots; residue systems (11A07)
Cites Work
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- Some \(q\)-analogues of supercongruences of Rodriguez-Villegas
- A \(q\)-microscope for supercongruences
- A supercongruence conjecture of Rodriguez-Villegas for a certain truncated hypergeometric function.
- Supercongruences concerning truncated hypergeometric series
- Further \(q\)-analogues of the (G.2) supercongruence of Van Hamme
- A \(q\)-supercongruence from a \(q\)-analogue of Whipple's \({}_3F_2\) summation formula
- \(q\)-supercongruences on triple and quadruple sums
- \(q\)-analogues of the (E.2) and (F.2) supercongruences of van Hamme
- Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions
- \(q\)-supercongruences from gasper and Rahman's summation formula
- Further generalizations of four supercongruences of Rodriguez-Villegas
- Some \(q\)-supercongruences from Gasper's Karlsson-Minton type summation
- An extension of a supercongruence of Long and Ramakrishna
- Some congruences from the Karlsson-Minton summation formula
- Some new results about 𝑞-trinomial coefficients
- Some congruences that extend Van Hamme's (D.2) supercongruence
- A GENERALISATION OF A SUPERCONGRUENCE ON THE TRUNCATED APPELL SERIES
- Some new \(q\)-supercongruences involving one free parameter
Related Items (4)
Proof of two conjectures of Guo and of Tang ⋮ Some parametric \(q\)-supercongruences from a summation of Gasper and Rahman ⋮ Divisibility of certain sums involving central \(q\)-binomial coefficients ⋮ \(q\)-supercongruences from Watson's \(_8 \phi_7\) transformation
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