On $q$-analogues of some series for $\pi $ and $\pi ^2$

DOI10.1090/proc/14374zbMath1441.05027arXiv1802.01506OpenAlexW2788481193MaRDI QIDQ4630648

Zhi-Wei Sun, Qing-Hu Hou, Christian Krattenthaler

Publication date: 23 April 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.01506

zbMATH Keywords

\(q\)-seriesidentityWZ methodseries for \(\pi\) and \(\pi^2\)

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Binomial coefficients; factorials; (q)-identities (11B65) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (8)

Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series ⋮ \(q\)-analogues of some series for powers of \(\pi\) ⋮ On two double series for \(\pi\) and their \(q\)-analogues ⋮ How to Generate All Possible Rational Wilf-Zeilberger Pairs? ⋮ \(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\) ⋮ $q$-analogues of several $\pi $-formulas ⋮ Some \(q\)-supercongruences from a quadratic transformation by Rahman ⋮ \(q\)-rational reduction and \(q\)-analogues of series for \(\pi\)

Cites Work

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• Hypergeometric series acceleration via the WZ method
• Super congruences and Euler numbers
• Hypergeometric identities for 10 extended Ramanujan-type series
• A \(q\)-analogue of the Bailey-Borwein-Bradley identity
• An Indefinite Bibasic Summation Formula and Some Quadratic, Cubic and Quartic Summation and Transformation Formulas
• q-Analogues of two Ramanujan-type formulas for 1/π

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