https://nova.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13147 Wed 24 Jul 2013 22:24:52 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 ]]> Energy of static electron lattices https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:13170 Sat 24 Mar 2018 08:16:05 AEDT ]]> The evaluation of character Euler double sums https://nova.newcastle.edu.au/vital/access/ /manager/Repository/uon:10334 Sat 24 Mar 2018 08:07:00 AEDT ]]>