q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64

DOI10.1142/S1793042121500056zbMath1479.33010OpenAlexW3043317804MaRDI QIDQ5857375

Xiaojing Chen, Chu, Wenchang

Publication date: 1 April 2021

Published in: International Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s1793042121500056

zbMATH Keywords

Ramanujan's series for \(1/\pi\)\(\pi\)-related infinite seriesBailey's well-poised \({}_6\pi_6\)-seriesGuillera's series for \(\pi^{\pm2}\)

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) (q)-gamma functions, (q)-beta functions and integrals (33D05)

Related Items (1)

ON GUILLERA’S -SERIES FOR

Cites Work

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• A new Ramanujan-like series for \(1/\pi ^{2}\)
• \(\pi \)-formulas implied by Dougall's summation theorem for \(_{5} F _{4}\)-series
• \(q\)-extensions of Dougall's bilateral \(_2H_2\)-series
• Hidden \(q\)-analogues of Ramanujan-like \(\pi\)-series
• Generators of some Ramanujan formulas
• Dougall's \(_5F_4\) sum and the WZ algorithm
• \(q\)-series reciprocities and further \(\pi\)-formulae
• Hypergeometric identities for 10 extended Ramanujan-type series
• Lost in Translation
• Accelerating Dougall’s $_5F_4$-sum and infinite series involving $\pi $
• Dougall’s bilateral ₂𝐻₂-series and Ramanujan-like 𝜋-formulae
• Partial sums of Bailey's₆ψ₆-series to faster convergent series
• Ramanujan-type formulae for $1/\pi$: A second wind?
• Proofs of some Ramanujan series for 1/π using a program due to Zeilberger
• About a New Kind of Ramanujan-Type Series
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS
• ON THE BASIC BILATERAL HYPERGEOMETRIC SERIES ₂ψ₂

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