22 citations · 57 across the 14 of their papers we have counts for
14 papers
Further Results on Vanishing Coefficients in Infinite Product Expansions
James Mc Laughlin
We extend results of Andrews and Bressoud on the vanishing of coefficients in the series expansions of certain infinite products. These results have the form that if \begin{equatio…
Refinements of Some Partition Inequalities
James Mc Laughlin
In the present paper we initiate the study of a certain kind of partition inequality, by showing, for example, that if is an integer and the integers and are rela…
Some new Transformations for Bailey pairs and WP-Bailey Pairs
James Mc Laughlin
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some…
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…
Hybrid Proofs of the -Binomial Theorem and other identities
Dennis Eichhorn, James Mc Laughlin, Andrew V. Sills
We give "hybrid" proofs of the -binomial theorem and other identities. The proofs are "hybrid" in the sense that we use partition arguments to prove a restricted version of the…
An Identity Motivated by an Amazing Identity of Ramanujan
James Mc Laughlin
Ramanujan stated an identity to the effect that if three sequences , and are defined by , $r_2(x)=:\sum_{n=0}^{\inft…