New characterizations of classical orthogonal polynomials
The authors reconsider the classical orthogonal polynomials (i.e., Jacobi, Laguerre, Hermite and Bessel polynomials) and give some new characterizations of them. The results are expressed in the form of two theorems which claim that some statements are equivalent to each other. The statements are extensions of the well-known characterizations which claim that (i) the classical orthogonal polynomials satisfy a second order linear differential equation and (ii) their derivatives of any fixed order are also orthogonal. The paper includes also a method to construct the linear differential equation corresponding to any classical orthogonal polynomial system.
scientific article; zbMATH DE number 941339