The Fibonacci Sequence via the sigma transform

Abstract

In this short article, we study different problems described as initial value problems of discrete differential equations and develop a a transform method called the sigma transform, a discrete version of the continuous Laplace transform to generate solutions as rational functions of integers to these initial value problems. Particularly we look how the method generates the traditionally known numbers called Fibonacci sequence as a solution to an initial value problem of a discrete differential equation.

12 pages on Fibonacci sequence and sigma transform