Important Relations of Classical Orthogonal Polynomials

In this thesis, the theory of classical orthogonal polynomials which are Hermite, Laguerre and Jacobi polynomials will be studied. To begin with, we will supply an outline regarding the special functions. Followed by examples of properties for orthogonal polynomials in Chapter 2. In the third chapter, we begin classical orthogonal polynomials. To start with, we collate the orthogonal relation, Rodrigues formulas followed by the norm of the classical orthogonal polynomials. In the same chapter, the division of the collected examples of classical orthogonal polynomials into three chapters and assign them the weight function, intermission of the orthogonality, followed by differential equations, hypergeometric representation. To finalise we explain limit relations between polynomials. Keywords: Classical orthogonal polynomials, hypergeometric functions, second order differential equations, Rodrigues formula.