The Cauchy Problem for Multidimensional Difference Equations in Lattice Cones

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

Picturing the Growth Order of Solutions in Complex Linear Differential–Difference Equations with Coefficients of φ-Order

“…Let us mention that, in fact, there is a significant amount of recent research on difference equations and their applications, as the ones developed in [18][19][20][21][22][23][24][25]. A number of authors (cf.…”