Lifting Bailey Pairs to WP-Bailey Pairs

Authors

James McLaughlin, West Chester University of PennsylvaniaFollow
Andrew Sills, Georgia Southern UniversityFollow
Peter Zimmer, West Chester University of Pennsylvania

Document Type

Article

Publication Date

8-28-2009

Publication Title

Discrete Mathematics

DOI

10.1016/j.disc.2009.03.015

ISSN

0012-365X

Abstract

A pair of sequences (α_n(a,k,q),β_n(a,k,q)) such that α₀(a,k,q)=1 and β_n(a,k,q)=∑ⁿ_j=0 (k/a;q)_n−j (k;q)_n+j / (q;q)_n−j (aq;q)_n+j α_j (a,k,q) is termed a WP-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.

Comments

This is a preprint of the final published article available at Discrete Mathematics.

Recommended Citation

McLaughlin, James, Andrew Sills, Peter Zimmer. 2009. "Lifting Bailey Pairs to WP-Bailey Pairs." Discrete Mathematics, 309 (16): 5077-5091. doi: 10.1016/j.disc.2009.03.015
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/166