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Article
Lifting Bailey Pairs to WP-Bailey Pairs
Discrete Mathematics
  • James McLaughlin, West Chester University of Pennsylvania
  • Andrew Sills, Georgia Southern University
  • Peter Zimmer, West Chester University of Pennsylvania
Document Type
Article
Publication Date
1-1-2009
Abstract

A pair of sequences (αn(a,k,q),βn(a,k,q)) such that α0(a,k,q)=1 and βn(a,k,q)=∑nj=0(k/a;q)n−j(k;q)n+j(q;q)n−j(aq;q)n+jαj(a,k,q) is termed aWP-Bailey Pair . Upon setting k=0 in such a pair we obtain a Bailey pair. In the present paper we consider the problem of “lifting” a Bailey pair to a WP-Bailey pair, and use some of the new WP-Bailey pairs found in this way to derive some new identities between basic hypergeometric series and new single-sum and double-sum identities of the Rogers–Ramanujan–Slater type.

Publisher
Elsevier
DOI
10.1016/j.disc.2009.03.015
Citation Information
James McLaughlin, Andrew Sills and Peter Zimmer. "Lifting Bailey Pairs to WP-Bailey Pairs" Discrete Mathematics Vol. 309 Iss. 16 (2009) p. 5077 - 5091 ISSN: 0012-365X
Available at: http://works.bepress.com/james-mclaughlin/5/