This article is cited in 2 papers

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

T. I. Nekrasova

Siberian Federal University, 79, Svobodny Prospect, Krasnoyarsk, 660041

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