25 citations · 72 across the 7 of their papers we have counts for
7 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…
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 Observations on Khovanskii's Matrix Methods for extracting Roots of Polynomials
James Mc Laughlin, B. Sury
In this article we apply a formula for the -th power of a matrix (found previously by the authors) to investigate a procedure of Khovanskii's for finding the cube ro…
Powers of a matrix and combinatorial identities
James Mc Laughlin, B. Sury
In this article we obtain a general polynomial identity in variables, where is an arbitrary positive integer. We use this identity to give a closed-form expression fo…
The Convergence and Divergence of -Continued Fractions outside the Unit Circle
Douglas Bowman, James Mc Laughlin
We consider two classes of -continued fraction whose odd and even parts are limit 1-periodic for , and give theorems which guarantee the convergence of the continued frac…
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…