On two double series for \(\pi\) and their \(q\)-analogues

DOI10.1007/s11139-022-00615-yOpenAlexW4292117572MaRDI QIDQ2689942

Chuanan Wei

Publication date: 14 March 2023

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

Full work available at URL: https://doi.org/10.1007/s11139-022-00615-y

zbMATH Keywords

hypergeometric series\(q\)-analoguebasic hypergeometric seriespartial derivative operatordouble series for \(\pi\)

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (2)

Infinite series about harmonic numbers inspired by Ramanujan-like formulae ⋮ Infinite series of convergence rate $-1/8$ suggested by two formulae of Guillera

Cites Work

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• On the supercongruence conjectures of van Hamme
• Hypergeometric evaluation identities and supercongruences
• Generators of some Ramanujan formulas
• Wronskians of theta functions and series for \(1/\pi\)
• Domb's numbers and Ramanujan-Sato type series for \(1/\pi\)
• \(q\)-analogues of three Ramanujan-type formulas for \(1/\pi\)
• A common \(q\)-analogue of two supercongruences
• A \(q\)-analogue for Euler's evaluations of the Riemann zeta function
• \(q\)-analogues of some series for powers of \(\pi\)
• A new series for π³and related congruences
• GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π
• More Ramanujan-type formulae for $ 1/\pi^2$
• Strange Evaluations of Hypergeometric Series
• Ramanujan-type formulae for 1/π: q-analogues
• A q-analogue of the (I.2) supercongruence of Van Hamme
• On $q$-analogues of some series for $\pi $ and $\pi ^2$
• q-Analogues of two Ramanujan-type formulas for 1/π
• Some q-congruences on double basic hypergeometric sums
• Two $q$-analogues of Euler’s formula $\zeta (2)=\pi ^2/6$
• Towards computerized proofs of identities

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