19 citations · 57 across the 9 of their papers we have counts for
9 papers
Rogers-Ramanujan-Slater Type Identities
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
In this survey article, we present an expanded version of Lucy Slater's famous list of identities of the Rogers-Ramanujan type, including identities of similar type, which were dis…
A Reciprocity Relation for WP-Bailey Pairs
James Mc Laughlin, Peter Zimmer
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several cons…
General WP-Bailey Chains
James Mc Laughlin, Peter Zimmer
Motivated by a recent paper of Liu and Ma, we describe a number of general WP-Bailey chains. We show that many of the existing WP-Bailey chains (or branches of the WP-Bailey tree),…
Some Applications of a Bailey-type Transformation
James Mc Laughlin, Peter Zimmer
If is set equal to in the definition of a WP Bailey pair, \[ β_{n}(a,k) = \sum_{j=0}^{n} \frac{(k/a)_{n-j}(k)_{n+j}}{(q)_{n-j}(aq)_{n+j}}α_{j}(a,k), \] this equation redu…
Lifting Bailey Pairs to WP-Bailey Pairs
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
A pair of sequences such that and \[ β_{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}}α_{j}(a,k,…
Some Implications of the WP-Bailey Tree
James Mc Laughlin, Peter Zimmer
We consider a special case of a WP-Bailey chain of George Andrews, and use it to derive a number of curious transformations of basic hypergeometric series. We also derive two new W…