Geodesic
On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations
The Bulletin of Irkutsk State University. Series Mathematics, Tome 9 (2014), pp. 91-102

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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. 
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     author = {T. I. Nekrasova},
     title = {On the {Hierarchy} of {Generating} {Functions} for {Solutions} of {Multidimensional} {Difference} {Equations}},
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T. I. Nekrasova. On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations. The Bulletin of Irkutsk State University. Series Mathematics, Tome 9 (2014), pp. 91-102. http://geodesic.mathdoc.fr/item/IIGUM_2014_9_a7/