25 citations · 69 across the 8 of their papers we have counts for
8 papers
On a pair of identities from Ramanujan's lost notebook
James Mc Laughlin, Andrew V. Sills
Using a pair of two variable series-product identities recorded by Ramanujan in the lost notebook as inspiration, we find some new identities of similar type. Each identity immedia…
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…
Polynomial Generalizations of two-variable Ramanujan type identities
James Mc Laughlin, Andrew V. Sills
We provide finite analogs of a pair of two-variable -series identities from Ramanujan's lost notebook and a companion identity.
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,…
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…
Combinatorics of Ramanujan--Slater type identities
James Mc Laughlin, Andrew V. Sills
We provide the missing member of a family of four -series identities related to the modulus 36, the other members having been found by Ramanujan and Slater. We examine combinato…