International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 4, Pages 271-277

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

Received 2 July 1998

Copyright © 2000 Geoffrey B. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.