A note on general solutions to a hyperbolic-cotangent class of systems of difference equations

Abstract

Recently there has been some interest in difference equations and systems whose forms resemble some trigonometric formulas. One of the classes of such systems is the so-called hyperbolic-cotangent class of systems of difference equations. The corresponding two-dimensional class has two delays denoted by k and l. So far the class has been studied for the case k≠ l, and it was shown that it is practically solvable when max { k, l} ≤ 2. In this note we show practical solvability of the system in the case k= l, not only for small values of k and l, but for all k= l∈ N, which is the first result of such generality.