A criterion for the applicability of Zeilberger's algorithm to rational functions
type: Item
instance of: scholarly article
title: A criterion for the applicability of Zeilberger's algorithm to rational functions
zbMATH Open document ID: 1023.33017
DOI: 10.1016/S0012-365X(02)00442-9
author: Yanyan Li
published in: Discrete Mathematics
publication date: 2003-03-16T00:00:00Z
review text: The applicability of Zeilberger's algorithm is considered and complete solutions are given for the case where the original hypergeometric term \(F(n,k)\) is a rational function. A class of identities \(\sum_{k=0}^n F(n,k)=0\) is specified that cannot be proven by Zeilberger's algorithm. Examples are discussed 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. The algorithms are compared with existing Maple codes.
Mathematics Subject Classification ID: 33F10
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 1882138
zbMATH Keywords: Zeilberger's algorithm
zbMATH Keywords: hypergeometric term
zbMATH Keywords: rational function
zbMATH Keywords: terminating condition
zbMATH Keywords: linear difference operator
zbMATH Keywords: \(q\)-difference operator
zbMATH Keywords: decomposition of indefinite sum
reviewed by: Nico M. Temme
describes a project that uses: Maple
MaRDI profile type: Publication
full work available at URL: s0012-365x(02)00442-9
OpenAlex ID: W2034438073
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description: scientific article; zbMATH DE number 1882138