More on a hyperbolic-cotangent class of difference equations

Abstract

© 2019 John Wiley & Sons, Ltd. We present a natural method for solving the difference equation. (Formula presented.) where k, l ∈ N, parameter a, and initial values x −j , (Formula presented.), (Formula presented.), are real or complex numbers. As a concrete example, the case k = 1, l = 2 is studied in detail, and several interesting formulas for solutions and objects used in the analysis of the equation are given. A useful remark on solvability of difference equations on complex domains is presented and used here.