Classical Continuous Orthogonal Polynomials

Classical orthogonal polynomials (Hermite, Laguerre, Jacobi and Bessel) constitute the most important families of orthogonal polynomials. They appear in mathematical physics when Sturn-Liouville problems for hypergeometric differential equation are studied. These families of orthogonal polynomials have specific properties. Our main aim is to: 1. recall the definition of classical continuous orthogonal polynomials; 2. prove the orthogonality of the sequence of the derivatives; 3. prove that each element of the classical orthogonal polynomial sequence satisfies a second-order linear homogeneous differential equation; 4. give the Rodrigues formula.