An interesting case of variables separation Original Research Article

We develop an alternative approach to the construction of explicit solutions for linear constant coefficient PDE of an arbitrary dimension. It is based upon generalization of classic results in the theory of functions of several complex variables and leads to algorithms for symbolic calculations. We prove a theorem on the convergence of series form solution and discuss an important and frequent case when the solutions are presented as finite sums. A particular solution for nonhomogeneous wave equation is found as an example.