https://nova.newcastle.edu.au/vital/access/ /manager/Index en-au 5 Elliptic integral representation of Bessel moments https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:6446 Wed 11 Apr 2018 16:50:58 AEST ]]> Lattice sums arising from the Poisson equation https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:12924 n(r₁,...,rn) = 1/π²[formula could not be replicated]. By virtue of striking connections with Jacobi ϑ-function values, we are able to develop new closed forms for certain values of the coordinates rk, and extend such analysis to similar lattice sums. A primary result is that for rational x, y, the natural potential ⏀²(x, y) is 1/π log A where A is an algebraic number. Various extensions and explicit evaluations are given. Such work is made possible by number-theoretical analysis, symbolic computation and experimental mathematics, including extensive numerical computations using up to 20,000-digit arithmetic.]]> Sat 24 Mar 2018 10:37:10 AEDT ]]> Integrals of the Ising Class https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:6447 Sat 24 Mar 2018 10:23:28 AEDT ]]> Energy of static electron lattices https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13170 Sat 24 Mar 2018 08:16:05 AEDT ]]> A five-dimensional extension of general relativity and quantum theory https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:9936 Sat 24 Mar 2018 08:14:17 AEDT ]]> Chebyshev type lattice path weight polynomials by a constant term method https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:11720 Sat 24 Mar 2018 08:07:25 AEDT ]]>