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

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