Some applications of Gasper's bibasic summation
type: Item
instance of: scholarly article
title: Some applications of Gasper's bibasic summation
zbMATH Open document ID: 1165.33012
DOI: 10.1216/RMJ-2008-38-2-703
author: Yusen Zhang
author: Tianming Wang
published in: Rocky Mountain Journal of Mathematics
publication date: 2009-04-07T00:00:00Z
review text: The main result is the bibasic summation formula \[ \begin{multlined} \sum_{k=0}^n(-1)^k\frac{(1-d)(1-ad/b)(1-ad^2q^{2k}/b)}{(1-dq^k)(1-adq^k/b)}\, \\ \times \frac{(ad^2/b;q)_k(adq^k;p)_n(b/dq^k;p)_n}{(q;q)_k(q;q)_{n-k}(ad^2/b;q)_{n+k+1}} \,q^{k(k+1)/2} =\frac{(a;p)_n(b;p)_n}{(dq;q)_n(adq/b;q)_n}, \end{multlined} \] where the \(q\)-shifted factorial is defined by \((a;q)_n=\prod_{j=0}^{n-1}(1-aq^j)\), and its applications to basic hypergeometric series. Another bibasic summation formula, announced in the introduction as equation~(3.5), is not given in the paper.
reviewed by: Wadim Zudilin
Mathematics Subject Classification ID: 33D15
Mathematics Subject Classification ID: 15A09
zbMATH DE Number: 5541241
zbMATH Keywords: inverse relation
zbMATH Keywords: basic hypergeometric series
zbMATH Keywords: bibasic summation formula
zbMATH Keywords: transformation formula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5541241