On rational definite summation

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 $S(n)={\sum }_{k=0}^{n-1}R(k,n)$.

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