Definite Sums as Solutions of Linear Recurrences With Polynomial Coefficients

04/09/2018

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by   Marko Petkovšek, et al.

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We present an algorithm which, given a linear recurrence operator L with polynomial coefficients, m ∈N∖{0}, a_1,a_2,...,a_m ∈N∖{0} and b_1,b_2,...,b_m ∈K, returns a linear recurrence operator L' with rational coefficients such that for every sequence h, L(∑_k=0^∞∏_i=1^m a_i n + b_ik h_k) = 0 if and only if L' h = 0.