19 citations · 40 across the 5 of their papers we have counts for
5 papers
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…
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 identities between basic hypergeometric series deriving from a new Bailey-type transformation
James Mc Laughlin, Peter Zimmer
We prove a new Bailey-type transformation relating WP-Bailey pairs. We then use this transformation to derive a number of new 3- and 4-term transformation formulae between basic hy…
Rogers--Ramanujan computer searches
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
We describe three computer searches (in PARI/GP, Maple, and Mathematica, respectively) which led to the discovery of a number of identities of Rogers-Ramanujan type and identities…