Six-variable generalization of Ramanujan's reciprocity theorem and its variants

DOI10.1016/j.jmaa.2008.11.039zbMath1185.33020OpenAlexW1971230281MaRDI QIDQ1014695

Xin Rong Ma

Publication date: 29 April 2009

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2008.11.039

zbMATH Keywords

\(q\)-seriesreciprocity theoremBailey's \(_{6\psi 6}\) summation formulaSears' transformation formulaShukla's \(_{8\psi 8}\) summation formulaWatson's transformation formula

Mathematics Subject Classification ID

Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15)

Related Items (9)

Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral ⋮ A symmetric generalization of an identity of Andrews and Yee ⋮ A Chaundy-Bullard type identity involving the Pochhammer symbol ⋮ A new proof of the Askey-Wilson integral via a five-variable Ramanujan's reciprocity theorem ⋮ Reciprocity theorems involving the \(q\)-gamma function ⋮ A note on four-variable reciprocity theorem ⋮ A symmetric formula for hypergeometric series ⋮ Several transformation formulas for basic hypergeometric series ⋮ Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral

Cites Work

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• Ramanujan's ``lost notebook. I: Partial Theta-functions
• Some operator identities and \(q\)-series transformation formulas
• A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook
• THE QUINTUPLE PRODUCT IDENTITY
• Generalizations of Ramanujan's reciprocity theorem and their applications

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