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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 4, Pages 805-810

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 Hindawi Publishing Corporation. 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.


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.