An interesting case of variables separation

We develop an alternative approach to the construction of explicit solution s for linear constant coefficient PDE of an arbitrary dimension. It is base d upon generalization of classic results in the theory of functions of seve ral complex variables and leads to algorithms for symbolic calculations. We prove a theorem on the convergence of series form solution and discuss a n important and frequent case when the solutions are presented as finite su ms. A particular solution for nonhomogeneous wave equation is found as an e xample. (C) 2000 Elsevier Science Ltd. All rights reserved.