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Summation in Finite Terms

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

Abstract

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.

Keywords

Order Linear Computer Algebra System Integration Problem Difference Field Finite Difference Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  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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