19 citations · 57 across the 10 of their papers we have counts for
10 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…
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…
Some more Long Continued Fractions, I
James Mc Laughlin, Peter Zimmer
In this paper we show how to construct several infinite families of polynomials , such that has a regular continued fraction expansion with arbi…
Some implications of Chu's extension of Bailey's summation formula
James Mc Laughlin, Andrew V. Sills, Peter Zimmer
Lucy Slater used Bailey's summation formula to derive the Bailey pairs she used to construct her famous list of 130 identities of the Rogers-Ramanujan type. In the present…
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…