Applicability of Zeilberger’s Algorithm to Rational Functions

S. A. Abramov () and H. Q. Le ()
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S. A. Abramov: Computer Center of the Russian Academy of Science
H. Q. Le: University of Waterloo, Symbolic Computation Group

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 91-102 from Springer

Abstract: 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 identities $$\sum\nolimits_{k = 0}^n {F\left( {n,k} \right) = 0} $$ $$F\left( {n,k} \right) \in \mathbb{C}\left( {n,k} \right)$$ that cannot be proven by Zeilberger’s algorithm. Additionally we give examples showing that the set of hypergeometric terms for 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.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_8

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