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 language | English |
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Pages (from-to) | 5077-5091 |
Number of pages | 15 |
Journal | Discrete Mathematics |
Volume | 309 |
Issue number | 16 |
DOIs | |
State | Published - 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