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Summation in Finite Terms

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Computer Algebra

Part of the book series: Computing Supplementum ((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.

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References

  1. Cohen, J., Katcoff, J.: Symbolic Solution of Finite Difference Equations. ACM Trans. Math. Software 3/3, 261–271 (1977).

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  2. Gosper, R. W., Jr.: Decision Procedure for Indefinite Hypergeometric Summation. Proc. Nat. Acad. Sci. USA 75/1, 40–42 (1978).

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  3. Jordan, C.: Calculus of Finite Differences. Sopron, Hungary: Röttig and Romwalter 1939.

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  4. Karr, M.: Summation in Finite Terms. Mass. Comput. Assoc. Inc. Wakefield, Mass.: Techn. Rep. CA-7602–1911, 1976.

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  5. Karr, M.: Summation in Finite Terms. J. ACM 28/2, 305–350 (1981).

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  6. Moenck, R.: On Computing Closed Forms for Summation. MACSYMA 1977, 225–236.

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Author information

Authors and Affiliations

  1. Centre de Calcul de l’Esplanade, Université Louis Pasteur, 7, rue René Descartes, F-67084, Strasbourg, France

    Prof. Dr. J. C. Lafon

Authors
  1. Prof. Dr. J. C. Lafon
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Editor information

Editors and Affiliations

  1. Institut für Mathematik, Johannes Kepler Universität Linz, Austria

    Bruno Buchberger

  2. Computer Science Department, University of Wisconsin-Madison, Madison, Wis., USA

    George Edwin Collins

  3. Institut für Informatik I, Universität Karlsruhe, Federal Republic of Germany

    Rüdiger Loos

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© 1982 Springer-Verlag Wien

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Lafon, J.C. (1982). Summation in Finite Terms. In: Buchberger, B., Collins, G.E., Loos, R. (eds) Computer Algebra. Computing Supplementum, vol 4. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3406-1_5

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  • DOI: https://doi.org/10.1007/978-3-7091-3406-1_5

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-81684-4

  • Online ISBN: 978-3-7091-3406-1

  • eBook Packages: Springer Book Archive

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