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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2014. Vol. 9

On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations

Author(s)
T. I. Nekrasova
Abstract

In this paper we study generating functions of solutions for a difference equation with the support in a rational cone of the lattice. For Laurent series with the support in such cone we define the notion of D-finiteness and find the sufficient condition, when rationality (algebraicity, D-finiteness) of the generating function of the solution to the Cauchy problem follows from rationality (algebraicity, D-finiteness) of the generating function of its initial data.

Keywords
multidimensional difference equations, Cauchy problem, generating function, D-finite Laurent series
UDC
517.55+517.96
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