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New Bounds for Hypergeometric Creative Telescoping

Published: 20 July 2016 Publication History

Abstract

Based on a modified version of Abramov-Petkovsek reduction, a new algorithm to compute minimal telescopers for bivariate hypergeometric terms was developed last year. We investigate further in this paper and present a new argument for the termination of this algorithm, which provides an independent proof of the existence of telescopers and even enables us to derive lower as well as upper bounds for the order of telescopers for hypergeometric terms. Compared to the known bounds in the literature, our bounds are sometimes better, and never worse than the known ones.

References

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S. A. Abramov and H. Le. On the order of the recurrence produced by the method of creative telescoping. Discrete Math., 298(1--3):2--17, 2005.
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S. A. Abramov and M. Petkovsek. Minimal decomposition of indefinite hypergeometric sums. In Proc. of ISSAC'01, pp. 7--14, 2001.
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S. A. Abramov and M. Petkovsek. Proof of a conjecture of Wilf and Zeilberger. Preprint Series of the Institute of Mathematics, Physics and Mechanics, University of Ljubljana, vol. 39, 2001.
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S. A. Abramov and M. Petkovsek. Rational normal forms and minimal decompositions of hypergeometric terms. J. Symbolic Comput., 33(5):521--543, 2002.
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M. Apagodu and D. Zeilberger. Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory. Adv. in Appl. Math., 37(2):139--152, 2006.
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S. Chen, H. Huang, M. Kauers, and Z. Li. A modified Abramov-Petkovsek reduction and creative telescoping for hypergeometric terms. In Proc. of ISSAC'15, pp. 117--124, 2015.
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S. Chen, M. Kauers, and C. Koutschan. Reduction-based creative telescoping for algebraic functions. To appear in Proc. of ISSAC'16, 2016.
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D. Zeilberger. The method of creative telescoping. J. Symbolic Comput., 11:195--204, 1991.

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cover image ACM Conferences
ISSAC '16: Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation
July 2016
434 pages
ISBN:9781450343800
DOI:10.1145/2930889
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Published: 20 July 2016

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  1. hypergeometric term
  2. modified Abramov-Petkovsek reduction
  3. order bound
  4. telescoper

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