Basic Analogue of Legendre Polynomial and its Difference Equation

The legendre polynomials belong to rich class of orthogonal polynomials which have been extensively investigated because of their applications in various fields. The main objective of this study was to derive the discrete Legendre polynomials as they represent the discrete functions or discrete data. In this study the difference equation of discrete Legendre polynomials was derived. Firstly, introduced the discrete Legendre polynomial of integer order about point s by using Taylors formula and some of its properties and later on it was shown that the current system satisfied Rodrigues formula.