James McLaughlinAffiliation: West Chester University of Pennsylvania Email: jmclaughl@wcupa.edu Title Of Talk: Lifting Bailey Pairs to WP-Bailey Pairs Abstract: A pair of sequences $(\wpalpha_{n}(a,k,q),\wpbeta_{n}(a,k,q))$ such that\\ $\wpalpha_0(a,k,q)=1$ and \[ \wpbeta_{n}(a,k,q) = \sum_{j=0}^{n} \frac{(k/a; q)_{n-j}(k; q)_{n+j}}{(q;q)_{n-j}(aq;q)_{n+j}}\wpalpha_{j}(a,k,q) \] is termed a \emph{WP-Bailey Pair}. Upon setting $k=0$ in such a pair we obtain a \emph{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.
Last update made Mon Mar 3 22:07:13 EST 2008.
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