\(q\)-derivative operators and basic hypergeometric series
type: Item
instance of: scholarly article
title: \(q\)-derivative operators and basic hypergeometric series
zbMATH Open document ID: 1108.33015
published in: Results in Mathematics
publication date: 2007-01-23T00:00:00Z
review text: The author obtains formal series expansions in terms of \(q\)-derivative operators. This generalizes some results due to \textit{L. Carlitz} [Glas. Mat. 28, 205--214 (1973; Zbl 0267.33010)] and \textit{Z.-G. Liu} [Ramanujan J. 6, 429--447 (2002; Zbl 1044.05012)]. As applications, he gets a non-termining summation formula for \({}_6\phi_5\)-series, at Watson's \(q\)-analogue transformation for \({}_8\phi_7\)-series, a basic hypergeometric transformation for \({}_8\phi_7\)-series and a reduction formula for the very-well-poised basic hypergeometric \({}_{10}\phi_9\)-series.
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 33D80
zbMATH DE Number: 5117885
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: \(q\)-derivative operator
zbMATH Keywords: Leibniz rule
zbMATH Keywords: inverse series relations
author: Wenchang Chu
reviewed by: Youssèf Ben Cheikh
MaRDI profile type: Publication
full work available at URL: s00025-006-0209-1
OpenAlex ID: W1653219948
DOI: 10.1007/S00025-006-0209-1
description: scientific article; zbMATH DE number 5117885