Lifting Bailey pairs to WP-Bailey pairs

A pair of sequences (αn(a,k,q),βn(a,k,q)) such that α0(a,k,q)=1 and βn(a,k,q)=∑j=0n(k/a;q)n−j(k;q)n+j(q;q)n−j(aq;q)n+jαj(a,k,q) is termed a WP-Bailey Pair  . Upon setting k=0k=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.