5 citations · 22 across the 8 of their papers we have counts for
8 papers
Apéry-like sequences defined by four-term recurrence relations
Shaun Cooper
The Apéry numbers may be defined by a cubic three-term recurrence relation, that is, a three-term relation where the coefficients are polynomials in the index of degree . In thi…
The Madelung Constant in Dimensions
Antony Burrows, Shaun Cooper, Peter Schwerdtfeger
We introduce two convergent series expansions (direct and recursive) in terms of Bessel functions and representations of sums of squares for -dimensional Madelung const…
Instability of the Body-Centered Cubic Lattice within the Sticky Hard Sphere and Lennard-Jones Model obtained from Exact Lattice Summations
Antony Burrows, Shaun Cooper, Peter Schwerdtfeger
A smooth path of rearrangement from the body-centered cubic (bcc) to the face-centered cubic (fcc) lattice is obtained by introducing a single parameter to cuboidal lattice vectors…
The Cuboidal Lattices and their Lattice Sums
Antony Burrows, Shaun Cooper, Peter Schwerdtfeger
Lattice sums of cuboidal lattices, which connect the face-centered with the mean-centered and the body-centered cubic lattices through parameter dependent lattice vectors, are eval…
Hypergeometric modular equations
Shaun Cooper, Wadim Zudilin
We record functional identities that, apart from being amazingly amusing by themselves, find applications in derivation of Ramanujan-…
Analogues of the Ramanujan--Mordell Theorem
Shaun Cooper, Ben Kane, Dongxi Ye
The Ramanujan--Mordell Theorem for sums of an even number of squares is extended to other quadratic forms and quadratic polynomials.