Lifting Bailey Pairs to WP-Bailey PairsDiscrete Mathematics
AbstractA 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.
Citation InformationJames 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/