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Finding telescopers with minimal depth for indefinite nested sum and product expressions

Published: 24 July 2005 Publication History

Abstract

We provide algorithms that find, in case of existence, indefinite nested sum extensions in which a (creative) telescoping solution can be expressed with minimal nested depth.

References

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C. Schneider. A collection of denominator bounds to solve parameterized linear difference equations in ΠΣ -extensions. In Proc. SYNASC04, pages 269--282, 2004. Mirton Publishing.
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C. Schneider. Symbolic summation with single-nested sum extensions. In J. Gutierrez, editor,Proc.~ISSAC'04}, pages 282--289. ACM Press, 2004.
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C. Schneider. Product representations in ΠΣ-fields. Annals of Combinatorics, 9(1):75--99, 2005.
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C. Schneider. Solving parameterized linear difference equations in terms of indefinite nested sums and products. To appear in J. Differ. Equations Appl.
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C. Schneider. Finding telescopers with minimal depth for indefinite nested sum and product expressions (extended version). J. Kepler University, Linz. SFB-Report 2005-08, 2004.
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D. Zeilberger. A fast algorithm for proving terminating hypergeometric identities. Discrete Math., 80(2):207--211, 1990.

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  1. Finding telescopers with minimal depth for indefinite nested sum and product expressions

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    cover image ACM Conferences
    ISSAC '05: Proceedings of the 2005 international symposium on Symbolic and algebraic computation
    July 2005
    388 pages
    ISBN:1595930957
    DOI:10.1145/1073884
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    New York, NY, United States

    Publication History

    Published: 24 July 2005

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    Author Tags

    1. difference fields
    2. symbolic summation

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