Simplification of definite sums of rational functions by creative symmetrizing method

摘要

We propose a strategy for simplification of definite sums of rational functions which, for a given input rational function F(n, k), constructs two rational functions G(n) and T(n, k) such that∑k=0ⁿF(n, k) = G(n) + ∑k=0ⁿT(n, k),where the degree of the denominator w.r.t. k of T(n, k) is "small". The strategy is based on well-known algorithms which solve the indefinite sum of rational functions and on the creative symmetrizing method. It provides a tool for finding closed forms for some instances of definite sums of rational functions where Zeilberger's creative telescoping method is not applicable.