Effective bounds for P-recursive sequences

We describe an algorithm that takes as input a complex sequence (u(n)) given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound (v(n)) such that vertical bar u(n)vertical bar <= v(n) for all n. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of u(n). We discuss applications to the evaluation of power series with guaranteed precision. (C) 2010 Elsevier Ltd. All rights reserved.