Classical Orthogonal Polynomials and Differential Operators

In this thesis we introduce the concept of classical orthogonal polynomials which are Hermite, Laguerre and Jacobi polynomials. We first provide the necessary overview on special functions. Then we give several properties of orthogonal polynomials in Chapter 2. In Chapter 3, we start to classical orthogonal polynomials firstly we obtain the orthogonality relation, Rodrigues formulas and we give the norm of the classical orthogonal polynomials. Finally we divide the examples of classical orthogonal polynomials into three chapters and for each of them we give the weight function, interval of the orthogonality, second order differential equation, hypergeometric representation. Keywords: classical orthogonal polynomials, hypergeometric function, second order differential equation, Rodrigues formula.