Document Type
Article
Publication Date
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.
Publication Title
Discrete Mathematics
ISSN
0012-365X
Publisher
Elsevier
Volume
309
Issue
16
First Page
5077
Last Page
5091
DOI
10.1016/j.disc.2009.03.015
Recommended Citation
McLaughlin, J., Sills, A., & Zimmer, P. (2009). Lifting Bailey Pairs to WP-Bailey Pairs. Discrete Mathematics, 309(16), 5077-5091. http://dx.doi.org/10.1016/j.disc.2009.03.015