A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
DOI10.1016/j.jmaa.2017.09.022zbMath1373.05025OpenAlexW2755152028MaRDI QIDQ1674411
Publication date: 2 November 2017
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2017.09.022
cyclotomic polynomials\(q\)-binomial coefficientsWilf-Zeilberger method\(q\)-WZ pair\(q\)-Chu-Vandermonde summation
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) Congruences; primitive roots; residue systems (11A07) Calculation of integer sequences (11Y55)
Related Items (46)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Some congruences on conjectures of van Hamme
- Some congruences on \(q\)-Catalan numbers
- On the supercongruence conjectures of van Hamme
- \(q\)-analogs of some congruences involving Catalan numbers
- The Rodriguez-Villegas type congruences for truncated \(q\)-hypergeometric functions
- Hypergeometric evaluation identities and supercongruences
- Some \(q\)-analogues of supercongruences of Rodriguez-Villegas
- Generators of some Ramanujan formulas
- Some congruences involving central \(q\)-binomial coefficients
- Ramanujan-type supercongruences
- A trinomial analogue of Bailey's lemma and \(N=2\) superconformal invariance
- \(q\)-analogs of the binomial coefficient congruences of Babbage, Wolstenholme and Glaisher
- \(q\)-analogue of a binomial coefficient congruence
- A generalization of Morley's congruence
- Some binomial series obtained by the WZ-method
- Products and sums divisible by central binomial coefficients
- Some arithmetic properties of the \(q\)-Euler numbers and \(q\)-Salié numbers
- Factors of the Gaussian coefficients
- Congruence properties of ordinary and q-binomial coefficients
- The \(q\)-Markov-WZ method
- Some q-analogs of congruences for central binomial sums
- A q-analog of Ljunggren's binomial congruence
- Some q-supercongruences for truncated basic hypergeometric series
- A $p$-adic supercongruence conjecture of van Hamme
- The power of a prime that divides a generalized binomial coefficient.
- A q-analogue of Lehmer's congruence
- A q-analogue of Apagodu–Zeilberger congruence
- A q-Analogue of Wolstenholme's Harmonic Series Congruence
This page was built for publication: A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients