A q-analogue of Appell's \(F_ 1\) function and some quadratic transformation formulas for non-terminating basic hypergeometric series
type: Item
instance of: scholarly article
title: A q-analogue of Appell's \(F_ 1\) function and some quadratic transformation formulas for non-terminating basic hypergeometric series
zbMATH Open document ID: 0594.33004
DOI: 10.1216/RMJ-1986-16-1-63
author: B. Nassrallah
author: Mizan Rahman
published in: Rocky Mountain Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A q-extension of Appell's integral representation of the double series \(F_ 1\) is given using the four parameter q-beta kernel times two \({}_ 1\phi_ 0's\). This integral is evaluated as the sum of three very well poised \(_{10}\phi_ 9's\). One limit as \(q\to 1\) gives the sum of three very well poised \({}_ 9F_ 8's\) as an integral. I do not understand why these results exist, but they are very interesting. Some interesting corollaries are quadratic transformations between very well poised \(_{10}\phi_ 9's\) and balanced \({}_ 5\phi_ 4's\).
Mathematics Subject Classification ID: 33D05
zbMATH DE Number: 3955415
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: q-series
zbMATH Keywords: quadratic transformations
reviewed by: R. Askey
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3955415