Third-Order Product-Type Systems of Difference Equations Solvable in Closed Form

Abstract

It is shown that a class of third order product-type systems of difference equations is solvable in closed form if initial values and multipliers are complex numbers, whereas the exponents are integers, by finding the formulas for the general solution in all possible cases. The main results complement some quite recent ones in the literature. The presented class of systems is the last one for whose investigation is not needed use of some associated polynomials of degree three or more, completing the investigation of such product-type systems.