On rational definite summation
<|reference_start|>On rational definite summation: 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)$.<|reference_end|>
@article{tsarev2004on,
    title={On rational definite summation},
    author={Sergey P. Tsarev},
    journal={arXiv preprint arXiv:cs/0407059},
    year={2004},
    archivePrefix={arXiv},
    eprint={cs/0407059},
    primaryClass={cs.SC cs.DM}
}