Expansions in terms of generalized helmholtz polynomials and associated functions

摘要

In this paper, necessary and sufficient conditions are developed to enable solutions of the equationto be expanded in terms of a set of polynomial solutions and their associated functions. The domain of validity for the polynomial expansion is for whole x-t plane; whereas the expansions in associated fucntions are confined to the hald-plane t2#x3F5;#x3C3; where #x3C3; is a positive constant.