Polynomial Expansions of Solutions of Cauchy Problems That Involve One Space Variable

Polynomial sets and polynomial expansion theorems are developed for solutions of Cauchy problems of the form ­ nu x, t.r­ t ns"Dmu x, t., ­ ju x, t.r­ t j < ts0 sfj x., js0, 1, . . . , ny1. If m)n, then the data functions must be entire of growth r ssr sy1. where ssmrn if n divides m and of growth r s sq1.rs if msnsqr where 1FrFny1. If nGm, then R-analyticity of the fj x. will suffice.