Particular Solutions of Linear Differential and (q-) Difference Systems with Hypergeometric Right-hand Sides

Abstract

Nonhomogeneous systems of linear ordinary differential, difference, and q-difference equations are considered. The coefficients of the systems are rational functions of one variable over a field of characteristic 0. Equations in the system may have arbitrary orders. For differential systems with a hyperexponential right-hand side and (q-)difference systems with a hypergeometric right-hand side, an algorithm for searching particular solutions is suggested. The search for a particular solution for such systems reduces to solving several problems of searching particular solutions of nonhomogeneous systems with polynomial coefficients and polynomial right-hand sides. An implementation of the algorithm in Maple 2018 is proposed.