The Cauchy Problem for Multidimensional Difference Equations in Lattice Cones

Abstract

Received 21.12.2019, received in revised form 26.01.2020, accepted 03.02.2020 Abstract. We consider a variant of the Cauchy problem for a multidimensional difference equation with constant coefficients, which connected with a lattice path problem in enumerative combinatorial analysis. We obtained a formula in which generating function of the solution to the Cauchy problem is expressed in terms of generating functions of the Cauchy data and a formula expressing solution to the Cauchy problem through its fundamental solution and Cauchy data.