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Direct Indefinite Summation

Published: 05 February 2015 Publication History
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References

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S. A. Abramov. The summation of rational functions. ?Z. Vy?cisl. Mat. i Mat. Fiz., 11:1071--1075, 1971.
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G. Boole. A Treatise on the Calculus of Finite Differences. Cambridge Library Collection. Cambridge University Press, Cambridge, 2009. Reprint of the 1860 original.
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A. Bostan, F. Chyzak, B. Salvy, and T. Cluzeau. Low complexity algorithms for linear recurrences. In Proceedings of the 2006 International Symposium on Symbolic and Algebraic Computation, ISSAC'06, pages 31--38, New York, NY, USA, 2006. ACM.
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Euler. Foundations of Differential Calculus. Springer-Verlag, New York, 2000. Translated from the Latin by John D. Blanton.
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J. Gerhard. Modular Algorithms in Symbolic Summation and Symbolic Integration, volume 3218 of Lecture Notes in Computer Science. Springer, 2004.
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J. Gerhard, M. Giesbrecht, A. Storjohann, and E. V. Zima. Shiftless decomposition and polynomialtime rational summation. In Proceedings of the 2003 International Symposium on Symbolic and Algebraic Computation, pages 119--126 (electronic), New York, 2003. ACM.
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R. W. Gosper, Jr. Indefinite hypergeometric sums in MACSYMA. In Proceedings of the 1977 MACSYMA Users' Conference, pages 237--251, 1977.
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R. W. Gosper, Jr. Decision procedure for indefinite hypergeometric summation. Proc. Nat. Acad. Sci. U.S.A., 75(1):40--42, 1978.
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M. Karr. Summation in finite terms. Journal of the Association for Computing Machinery, 28(2):305--350, 1981.
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J. C. Lafon. Summation in finite terms. In B. Buchberger, G. E. Collins, R. Loos, and R. Albrecht, editors, Computer algebra. Symbolic and algebraic computation, pages 71--77. Springer, Vienna, 1983.
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Y.-K. Man. On computing closed forms for indefinite summations. Journal of Symbolic Computation, 16(4):355--376, Oct. 1993.
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R. Moenck. On computing closed forms for summations. In Proceedings of the 1977 MACSYMA Users' Conference, pages 225--236, 1977.
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E. V. Zima. Accelerating indefinite summation: Simple classes of summands. Mathematics in Computer Science, 7(4):455--472, 2013.

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  1. Direct Indefinite Summation

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    cover image ACM Communications in Computer Algebra
    ACM Communications in Computer Algebra  Volume 48, Issue 3/4
    September/December 2014
    123 pages
    ISSN:1932-2232
    EISSN:1932-2240
    DOI:10.1145/2733693
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    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 05 February 2015
    Published in SIGSAM-CCA Volume 48, Issue 3/4

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