Simplification of definite sums of rational functions by creative symmetrizing method

  • Authors:

  • Ha Le

  • Affiliations:

  • University of Waterloo, Waterloo, Ontario, Canada

  • Venue:
  • Proceedings of the 2002 international symposium on Symbolic and algebraic computation
  • Year:
  • 2002

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Abstract

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.