ABSTRACT
Difference equations are equations involving discrete variables. They appear as natural descriptions of natural phenomena and in the study of discretization methods for differential equations, which have continuous variables. This typical equation describes the famous Fibonacci sequence. With a constant, the equation is solved by making the assumption value. An elegant way of solving linear difference equations with constant coefficients, among other applications, is by use of generating functions or, as an alternative, the z transform. Many of the orthogonal polynomials of differential equations and numerical analysis satisfy a second-order difference equation involving a discrete variable and a continuous variable.
