Abstract
Indefinite summation essentially deals with the problem of inverting the difference operator Δ: f( X) → f( X + 1) - f( X). In the case of rational functions over a field k we consider the following version of the problem: given α ϵ k( X), determine β, γ ϵ k ( X) such that α = Δβ+γ, where γ is as "small" as possible (in a suitable sense). In particular, we address the question: what can be said about the denominators of a solution (β, γ) by looking at the denominator of α only? An "optimal" answer to this question can be given in terms of the Gosper-Petkovšek representation for rational functions, which was originally invented for the purpose of indefinite hypergeometric summation. This information can be used to construct a simple new algorithm for the rational summation problem.
Published Version
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