International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 271-277
doi:10.1155/S0161171200000764
Infinite products over hyperpyramid lattices
Geoffrey B. Campbell
Centre for Mathematics and its Applications, School of Mathematical Sciences, Australian National University, ACT, Canberra 0200, Australia
Abstract
New infinite product identities are given, based on summed visible (from the origin) point vectors. Each result is found from summing on vpv lattices dividing space into radial regions from the origin. Recently, Baake et al. and Mosseri considered the 2-D visible lattice points as part of an optical experiment in which so-called Optical Fourier Transform was applied. Many of the techniques exposed by Glasser and Zucker, and Ninham et al. involving Mellin and Möbius inversions are also applicable to the current paper.