On rational definite summation

2004/07/24 by S. P. Tsarëv, Sergey P. Tsarev, Tsarev, Sergey P.
Computer Science · Mathematics · #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #History and Theory of Mathematics #I.1.2 #Mathematical and Theoretical Analysis #Mathematics and Applications #Symbolic Computation (cs.SC) #cs.DM #cs.SC

paper · pdf · doi:10.48550/arxiv.cs/0407059

LaTeX 2.09, 7 pages, submitted to "Programming & Computer Software"

arxiv created 2004/07/24 · openalex publication_date 2004/07/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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) = ∑_k=0^n-1R(k,n).

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