A criterion for the applicability of Zeilberger's algorithm to rational functions

Authors:
S. A. Abramov;H. Q. Le
Affiliations:
Computer Center of the Russian Academy of Science, Vavilova 40, Moscow 117967, Russia;Symbolic Computation Group, University of Waterloo, Waterloo, Canada N2L 3G1
Venue:
Discrete Mathematics
Year:
2002

Citing 10
Cited 3

The method of creative telescoping

Journal of Symbolic Computation
On the greatest common divisor of polynomials which depend on a parameter

ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
On Zeilberger's algorithm and its q-analogue

VII SPOA Proceedings of the seventh Spanish symposium on Orthogonal polynomials and applications
Indefinite sums of rational functions

ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Rational summation and Gosper-Petkovsˇek

Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
A Mathematica version of Zeilberger's algorithm for proving binomial coefficient identities

Journal of Symbolic Computation - Special issue on symbolic computation in combinatorics
Minimal decomposition of indefinite hypergeometric sums

Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Concrete Math

Concrete Math
On the q-Analogue of Zeilberger's Algorithm to Rational Functions

Programming and Computing Software
The automatic construction of pure recurrence relations

ACM SIGSAM Bulletin

A direct algorithm to construct the minimal Z-pairs for rational functions

Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
Applicability of the q-analogue of Zeilberger's algorithm

Journal of Symbolic Computation
Order-degree curves for hypergeometric creative telescoping

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation

Quantified Score

Hi-index	0.05

Visualization

Abstract

We consider the applicability (or terminating condition) of the well-known Zeilberger's algorithm and give the complete solution to this problem for the case where the original hypergeometric term F(n,k) is a rational function. We specify a class of identifies Σk=0nF(n,k)= 0, F(n,k) ∈ C(n,k), that cannot be proven by Zeilberger's algorithm. Additionally, we give examples showing that the set of hypergeometric terms on which Zeilberger's algorithm terminates is a proper subset of the set of all hypergeometric terms, but a super-set of the set of proper terms.