International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 805-810
doi:10.1155/S0161171293001000
Theta function identities from optical neural network transformations
Department E.C.M., Faculty of Physics, University of Barcelona, Diagonal 647, Barcelona 08028, Spain
Received 13 February 1992; Revised 12 May 1992
Copyright © 1993 E. Elizalde and A. Romeo. 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.
Abstract
We take a new approach to the generation of Jacobi theta function identities. It
is complementary to the procedure which makes use of the evaluation of Parseval-like identities
for elementary cylindrically-symmetric functions on computer holograms. Our method is more
simple and explicit than this one, which was an outcome of the construction of neurocomputer
architectures through the Heisenberg model.