Summation in Finite Terms

  • J. C. Lafon
Part of the Computing Supplementum book series (COMPUTING, volume 4)


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.


Order Linear Computer Algebra System Integration Problem Difference Field Finite Difference Equation 
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  1. [1]
    Cohen, J., Katcoff, J.: Symbolic Solution of Finite Difference Equations. ACM Trans. Math. Software 3/3, 261–271 (1977).MATHCrossRefGoogle Scholar
  2. [2]
    Gosper, R. W., Jr.: Decision Procedure for Indefinite Hypergeometric Summation. Proc. Nat. Acad. Sci. USA 75/1, 40–42 (1978).MathSciNetMATHCrossRefGoogle Scholar
  3. [3]
    Jordan, C.: Calculus of Finite Differences. Sopron, Hungary: Röttig and Romwalter 1939.Google Scholar
  4. [4]
    Karr, M.: Summation in Finite Terms. Mass. Comput. Assoc. Inc. Wakefield, Mass.: Techn. Rep. CA-7602–1911, 1976.Google Scholar
  5. [5]
    Karr, M.: Summation in Finite Terms. J. ACM 28/2, 305–350 (1981).MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    Moenck, R.: On Computing Closed Forms for Summation. MACSYMA 1977, 225–236.Google Scholar

Copyright information

© Springer-Verlag Wien 1982

Authors and Affiliations

  • J. C. Lafon
    • 1
  1. 1.Centre de Calcul de l’EsplanadeUniversité Louis PasteurStrasbourgFrance

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