Lifting Bailey pairs to WP-Bailey pairs

James McLaughlin, Andrew V. Sills, Peter Zimmer

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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) = underover(∑, j = 0, n) frac((k / a ; q)n - j (k ; q)n + j, (q ; q)n - j (a q ; q)n + j) αj (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.

Original languageEnglish
Pages (from-to)5077-5091
Number of pages15
JournalDiscrete Mathematics
Volume309
Issue number16
DOIs
StatePublished - Aug 28 2009

Scopus Subject Areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Keywords

  • Bailey chains
  • Bailey pairs
  • Rogers-Ramanujan type identities
  • WP-Bailey pairs
  • q-series

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