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This article is cited in 2 scientific papers (total 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.  Full text:
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UDC: 517.55+517.96 Citation: T. I. Nekrasova, “On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations”, The Bulletin of Irkutsk State University. Series Mathematics, 9 (2014), 
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