q-analogue of a transformation of Whipple
type: Item
instance of: scholarly article
title: q-analogue of a transformation of Whipple
zbMATH Open document ID: 0532.33003
DOI: 10.1216/RMJ-1983-13-4-639
author: N. E. Zubov
published in: Rocky Mountain Journal of Mathematics
publication date: 1983-01-01T00:00:00Z
review text: Of late, a great resurgence of interest in the theory of q-analogues of hypergeometric series has taken place. Here, the authors begin by first establishing a quite general formula where a particular bi-basic series on the bases q and \(q^ 2\) is expressed as a series involving the single base \(q^ 2\) with argument \(q^ 2\) of the form \({}_ 5\Phi_ 4\). By suitable specialisation of this result, q-analogues of two formulae of \textit{F. J. W. Whipple} [Proc. Lond. Math. Soc., II. Ser. 26, 257-272 (1927)] connecting nearly-poised \({}_ 4F_ 3\) and Saalschützian \({}_ 5F_ 4\) series are deduced. The rest of this most interesting paper is devoted to obtaining various new summation theorems and transformations for both basic hypergeometric series and their ordinary counterparts, again utilising the same main result. The formulae given in this paper seem generally to be rather too lengthy for explicit inclusion in a short review.
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 3844134
zbMATH Keywords: q-analogue of formulae of Whipple
zbMATH Keywords: summation theorems for basic hypergeometric series
zbMATH Keywords: nearly-poised hypergeometric series
reviewed by: H. Exton
MaRDI profile type: Publication
full work available at URL: rmj-1983-13-4-639
OpenAlex ID: W2070826984
description: scientific article; zbMATH DE number 3844134