Hypergeometric solutions of linear recurrences with polynomial coefficients
type: Item
instance of: scholarly article
title: Hypergeometric solutions of linear recurrences with polynomial coefficients
zbMATH Open document ID: 0761.11008
DOI: 10.1016/0747-7171(92)90038-6
published in: Journal of Symbolic Computation
publication date: 1993-01-16T00:00:00Z
review text: Let \(a(n)\) be a sequence over a field \(K\) of characteristic zero. We say that \(a(n)\) is hypergeometric if there is a rational function \(r(x) \in K(x)\) such that \(a(n+1) = r(n) a(n)\) for all sufficiently large integers \(n\). Given any linear recurrence with polynomial coefficients in \(K_ 0(n)\) and an extension field \(K\) of \(K_ 0\), the author presents an algorithm that will determine whether or not this recurrence has a hypergeometric solution over \(K\). He also describes an extension of the algorithm that will determine if there is a solution in the linear space spanned by the hypergeometric sequences. The algorithms explicitly construct solutions when they exist and, in the case of a homogeneous linear recurrence, a basis for the solution set.
Mathematics Subject Classification ID: 11B37
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 96018
zbMATH Keywords: linear recurrence with polynomial coefficients
zbMATH Keywords: algorithm
zbMATH Keywords: hypergeometric solution
Wikidata QID: Q55880087
author: Marko Petkovšek
reviewed by: David M. Bressoud
describes a project that uses: hyper
MaRDI profile type: Publication
full work available at URL: 0747-7171(92)90038-6
OpenAlex ID: W2119371075
cites work: Q3031846
cites work: Q3471654
cites work: Q3207312
cites work: Q5334359
cites work: Q4769056
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DBLP publication ID: journals/jsc/Petkovsek92
description: scientific article; zbMATH DE number 96018