The Cauchy function for \(n\)-th order linear difference equations (Q1898324)

The authors find the form of the Cauchy function for \(n\)-th order linear difference equations with real constant coefficients, as formulated in four theorems and six examples. A Cauchy function is the discrete solution of an initial value problem involving the highest order coefficient of a linear difference equation with real-valued variable coefficients. This function can be used to express the solution of an initial value problem for the corresponding nonhomogeneous linear difference equation.