\(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\)

DOI10.1007/s11139-018-0096-6zbMath1468.11066OpenAlexW3013648673MaRDI QIDQ1987613

Victor J. W. Guo

Publication date: 15 April 2020

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-018-0096-6

zbMATH Keywords

congruencesRamanujanWZ pair\(1/\pi\)

Mathematics Subject Classification ID

Factorials, binomial coefficients, combinatorial functions (05A10) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (16)

Double series expansions for \(\pi\) ⋮ Some \(q\)-supercongruences from transformation formulas for basic hypergeometric series ⋮ \(q\)-analogues of some series for powers of \(\pi\) ⋮ \(q\)-supercongruences modulo the fourth power of a cyclotomic polynomial via creative microscoping ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ Some new \(q\)-congruences on double sums ⋮ Unnamed Item ⋮ Proof of a \(q\)-supercongruence conjectured by Guo and Schlosser ⋮ Proof of a supercongruence conjectured by Sun through a \(q\)-microscope ⋮ $q$-analogues of several $\pi $-formulas ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ Some q-supercongruences for truncated forms of squares of basic hypergeometric series ⋮ Some q-congruences on double basic hypergeometric sums ⋮ A -ANALOGUE OF A DWORK-TYPE SUPERCONGRUENCE ⋮ \(q\)-rational reduction and \(q\)-analogues of series for \(\pi\) ⋮ Gosper summability of rational multiples of hypergeometric terms

Cites Work

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• Generators of some Ramanujan formulas
• Ramanujan-type supercongruences
• Hypergeometric series acceleration via the WZ method
• A \(q\)-analogue of the (L.2) supercongruence of van Hamme
• A \(q\)-analogue of the (J.2) supercongruence of van Hamme
• A \(q\)-analogue of a Ramanujan-type supercongruence involving central binomial coefficients
• A \(q\)-microscope for supercongruences
• Applications of q-Lagrange Inversion to Basic Hypergeometric Series
• Ramanujan-type formulae for 1/π: q-analogues
• On $q$-analogues of some series for $\pi $ and $\pi ^2$
• WZ pairs and q-analogues of Ramanujan series for 1/π
• q-Analogues of two Ramanujan-type formulas for 1/π
• Some Quadratic and Cubic Summation Formulas for Basic Hypergeometric Series

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