Some transformations on the bilateral series \(_2\psi_2\)
type: Item
instance of: scholarly article
title: Some transformations on the bilateral series \(_2\psi_2\)
zbMATH Open document ID: 1320.33028
DOI: 10.1216/RMJ-2014-44-5-1697
author: Zhizheng Zhang
author: Zeya Jia
published in: Rocky Mountain Journal of Mathematics
publication date: 2015-01-14T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.rmjm/1420071563
review text: The authors study the bilateral series \({}_2\psi_2\) and derive some transformation formulas in terms of unilateral basic hypergeometric series. First of all, they derive a transformation formula for a certain bilateral \({}_2\psi_2\) series as a linear combination of two unilateral \({}_2\phi_1\) series. This formula turns out to be a generalization of some known and new \(q\)-series identities, such as Ramanujan's \({}_1\psi_1\) summation formula and a certain \({}_2\psi_2\) summation formula. Secondly, the authors derive a transformation formula for a certain bilateral \({}_2\psi_2\) series as a linear combination of three unilateral \({}_2\phi_1\) series. This turns out to be a generalization of Bailey's \({}_2\psi_2\) summation formula for instance. Finally, they discuss some transformation formulas between bilateral \({}_2\psi_2\) and unilateral \({}_3\phi_2\) series. One of these generalizes the Bailey-Daum summation formula and a special case of Ramanujan's \({}_1\psi_1\) summation formula for instance. Furthermore, the authors refer to the paper \textit{Z. Zhang} and \textit{C. Zhang} [Util. Math. 92, 365--375 (2013; Zbl 1296.33030)] for another transformation formula between \({}_2\psi_2\) and \({}_3\phi_2\) series.
reviewed by: Roelof Koekoek
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 33D60
zbMATH DE Number: 6386244
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: bilateral series
zbMATH Keywords: unilateral series
zbMATH Keywords: \(q\)-Gauss summation formula
zbMATH Keywords: Bailey-Daum summation formula
MaRDI profile type: Publication
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OpenAlex ID: W2077961001
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description: scientific article; zbMATH DE number 6386244