Minimal decomposition of indefinite hypergeometric sums

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Minimal decomposition of indefinite hypergeometric sums

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2001 international symposium on Symbolic and algebraic computation table of contents

London, Ontario, Canada

Pages: 7 - 14

Year of Publication: 2001

ISBN:1-58113-417-7

Authors

Sergei A. Abramov	Computer Center of the Russian Academy of Science, Moscow, Russia
M. Petkovsek	Univ. of Ljubljana, Ljubljana, Slovenia

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 8, Downloads (12 Months): 15, Citation Count: 6

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ABSTRACT

We present an algorithm which, given a hypergeometric term T(n), constructs hypergeometric terms T1(n) and T2(n) such that T(n) = T1(n + 1) -T1(n) + T2(n), and T2(n) is minimal in some sense. This solves the decomposition problem for indefinite sums of hypergeometric terms: T1(n + 1) - T1(n) is the “summable part” and T2(n) the “non-summable part” of T(n).

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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	2	S. A. Abramov, Indefinite sums of rational functions, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.303-308, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220386]
	3	S. A. Abramov and M. Petkovek. Canonical representations of hypergeometric terms. In Proceedings FPSAC'01, 2001. To appear.
	4	R. W. Gosper. Decision procedure for indefinite hypergeometric summation. Proc. Natl. Acad. Sci. USA, 75:40-42, 1978.
	5	Peter Paule, Greatest factorial factorization and symbolic summation, Journal of Symbolic Computation, v.20 n.3, p.235-268, Sept. 1995 [doi>10.1006/jsco.1995.1049]
	6	M. Petkovek, H. S. Wilf, and D. Zeilberger. A=B. A K Peters, Wellesley, Massachusetts, 1996.
	7	Roberto Pirastu , Volker Strehl, Rational summation and Gosper-Petkovsˇek, Journal of Symbolic Computation, v.20 n.5-6, p.617-635, Nov./Dec. 1995 [doi>10.1006/jsco.1995.1068]

CITED BY 6

	S. A. Abramov , M. Petkovsek, Rational normal forms and minimal decompositions of hypergeometric terms, Journal of Symbolic Computation, v.33 n.5, p.521-543, May 2002
	H. Q. Le, A direct algorithm to construct the minimal Z-pairs for rational functions, Advances in Applied Mathematics, v.30 n.1/2, p.137-159, January 2003
	H. Q. Le, Computing the minimal telescoper for sums of hypergeometric terms, ACM SIGSAM Bulletin, v.35 n.3, September 2001
	S. A. Abramov, When does Zeilberger's algorithm succeed?, Advances in Applied Mathematics, v.30 n.3, p.424-441, April 2003
	S. A. Abramov , H. Q. Le, A criterion for the applicability of Zeilberger's algorithm to rational functions, Discrete Mathematics, v.259 n.1-3, p.1-17, 28 December 2002
	S. A. Abramov, Applicability of Zeilberger's algorithm to hypergeometric terms, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.1-7, July 07-10, 2002, Lille, France