Summing Symbols in Mutual Recurrences

摘要

The problem of summing a set of mutual recurrence relations with constant coefficients is investigated. A method is presented for summing an order d system of the form A(n) = Σ_(i=1)~d M_iA(n - i) + G(n), where A, G : N→ K~m and M_1,..., M_d ∈ M_m(K) for some field K and natural number m. The procedure expresses the sum Σ_i~n=0 A(i) in terms of A(n),..., A(n - d), initial conditions and sums of the inhomogeneous term G(n).