A note on an identity of Andrews
type: Item
instance of: scholarly article
title: A note on an identity of Andrews
zbMATH Open document ID: 1079.33013
author: Zhizheng Zhang
published in: The Electronic Journal of Combinatorics
publication date: 2005-04-25T00:00:00Z
full work available at URL: https://eudml.org/doc/125481
full work available at URL: v12i1n3.html
review text: In this paper, starting from an identity of \textit{G. E. Andrews} [Adv. Math. 41, 137--172 (1981; Zbl 0477.33001)] and using the \(q\)-exponential operator technique, the author derives , for \(0<| q| <1\), the following identity: \[ d\sum_{n=0}^{\infty}{\left(q/bc,q/ce,acdf;q\right)_n\over \left(ad,df;q\right)_{n+1} \left(q^2/bcde;q\right)_n}q^n- c\sum_{n=0}^{\infty}{\left(q/bd,q/de,acdf;q\right)_n\over \left(ac,cf;q\right)_{n+1} \left(q^2/bcde;q\right)_n}q^n \] \[ \qquad\qquad=d{\left(q,qd/c,c/d,abcd,acdf,bcdf,acde,cdef,bcde/q;q\right)_\infty\over \left(ac,ad,cf,df,bc,bd,ce,de,abc^2d^2ef/q;q\right)_\infty}. \]
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 05A30
zbMATH DE Number: 2161322
zbMATH Keywords: \(q\)-exponential operator
reviewed by: Youssèf Ben Cheikh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2161322