\(q\)-extensions of Dougall's bilateral \(_2H_2\)-series

DOI10.1007/s11139-010-9247-0zbMath1216.33030OpenAlexW2061743062MaRDI QIDQ539138

Chu, Wenchang

Publication date: 27 May 2011

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

Full work available at URL: https://doi.org/10.1007/s11139-010-9247-0

zbMATH Keywords

basic hypergeometric seriesAbel's lemma on summation by partsBailey's well-poised bilateral \({}_{6} \psi_{6}\)-seriesRogers-Fine identity

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

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Products of two ₁ϕ₁ series and implications ⋮ Nonterminating well–poised hypergeometric series ⋮ Q-analogues of five difficult hypergeometric evaluations ⋮ q-Analogues of Guillera’s two series for π±2 with convergence rate 27 64

Cites Work

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• Abel's method on summation by parts and well-poised bilateral \(_{5}\psi _{5}\)-series identities
• Abel's method on summation by parts and theta hypergeometric series
• Bilateral Bailey lemma and Rogers-Ramanujan identities
• Ramanujan's ``lost notebook. II: Theta-function expansions
• An expansion formula for \(q\)-series and applications
• Some basic bilateral sums and integrals
• Abel's lemma on summation by parts and basic hypergeometric series
• Bailey's very well-poised \(_6\psi_6\)-series identity
• A simple proof of Bailey’s very-well-poised ₆𝜓₆ summation
• Partial sums of Bailey's₆ψ₆-series to faster convergent series
• A q-EXTENSION OF CAUCHY'S FORM OF THE BETA INTEGRAL
• Partial fractions and bilateral summations
• SERIES OF HYPERGEOMETRIC TYPE WHICH ARE INFINITE IN BOTH DIRECTIONS
• ON THE BASIC BILATERAL HYPERGEOMETRIC SERIES ₂ψ₂

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