In this paper we have investigated the growth properties of solutions of the generalized axially symmetric, reduced wave equation in (n + 1) variables. Results analogus to those for order and type found in the theory of entire functions of several complex variables, of solutions, in terms of their expansion coefficients have been obtained. Our study is essential to a detailed understanding of the scattering of waves by central potentials and may be applied for generalized (n + 2)􀀀dimensional problems of potential scattering in quantum mechanics.

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