Solution of the general linear recurrence equation in C7 using a Bell polynomial

Abstract

We give solutions of two recurrence equations for an unknown xn in CR × S, given Vj,aj in CR × S and cn in Cr × s. The solutions are given in terms of a new type of multivariate Bell polynomial easily obtained from its univariate version. These solutions give no clue to the behavior for large n. That requires assumptions on the form of vn and an, Cn- Under certain assumptions on these, we show that xn is a weighted sum of nth powers.