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On rational definite summation

Sergey P. Tsarev
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Abstract

We present a partial proof of van Hoeij-Abramov conjecture about the algorithmic possibility of computation of finite sums of rational functions. The theoretical results proved in this paper provide an algorithm for computation of a large class of sums $ S(n) = \sum_{k=0}^{n-1}R(k,n)$.

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Sergey P. Tsarev. 2004-07-24. On rational definite summation. https://arxiv.org/abs/cs/0407059

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