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Summation in Finite Terms

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

Abstract

A survey on algorithms for summation in finite terms is given. After a precise defmition 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

Rational Function Order Linear Difference Field Finite Difference Equation Finite Term 
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

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

Copyright information

© Springer-Verlag/Wien 1983

Authors and Affiliations

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

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