Summation in Finite Terms
A survey on algorithms for summation in finite terms is given. After a precise definition of the problem the cases of polynomial and rational summands are treated. The main concern of this paper is a description of Gosper’s algorithm, which is applicable for a wide class of summands. Karr’s theory of extension difference fields and some heuristic techniques are touched on briefly.
KeywordsOrder Linear Computer Algebra System Integration Problem Difference Field Finite Difference Equation
Unable to display preview. Download preview PDF.
- Jordan, C.: Calculus of Finite Differences. Sopron, Hungary: Röttig and Romwalter 1939.Google Scholar
- Karr, M.: Summation in Finite Terms. Mass. Comput. Assoc. Inc. Wakefield, Mass.: Techn. Rep. CA-7602–1911, 1976.Google Scholar
- Moenck, R.: On Computing Closed Forms for Summation. MACSYMA 1977, 225–236.Google Scholar