# Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone

## Document Type

Article

## Publication Date

11-2022

## Abstract

We consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lattice Z π to find a recurrence relation (difference equation with polynomial coefficients) for the section of the generating series. This formula allows us to find a generating series of a solution to the Cauchy problem in the lattice cone through a generating series of its initial data and a right-side function of the difference equation. We derived an integral representation for sections of the holomorphic function, whose coefficients satisfy the difference equation with complex coefficients. Finally, we propose a system of differential equations for sections that represent D-finite functions of two complex variables.

## Recommended Citation

Lyapin A. P., Cuchta T. Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone. The Bulletin of Irkutsk State University. Series Mathematics, 2022, vol. 42, pp. 75β89. https://doi.org/10.26516/1997-7670.2022.42.75

## Comments

Published by Irkutsk State University.