WZ pairs and q-analogues of Ramanujan series for 1/π
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Publication:4646569
DOI10.1080/10236198.2018.1551380zbMath1405.11021arXiv1803.08477OpenAlexW2903350319MaRDI QIDQ4646569
Publication date: 14 January 2019
Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1803.08477
Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Generalized hypergeometric series, ({}_pF_q) (33C20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)
Related Items (17)
Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series ⋮ Double series expansions for \(\pi\) ⋮ Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ Further WZ-based methods for proving and generalizing Ramanujan's series ⋮ Proof of some \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial ⋮ Unnamed Item ⋮ Unnamed Item ⋮ \(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\) ⋮ Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser ⋮ $q$-analogues of several $\pi $-formulas ⋮ Proof of a generalization of the (B.2) supercongruence of Van Hamme through a \(q\)-microscope ⋮ Bilateral Ramanujan-like series for 1/πk and their congruences ⋮ 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 ⋮ A new extension of the (H.2) supercongruence of Van Hamme for primes \(p\equiv 3\operatorname{mod}{4}\)
Cites Work
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