Classical Orthogonal Polynomials

Abstract

Classical orthogonal Polynomials — the Jacobi, Laguerre and Hermite polynomials — form the simplest class of special functions. At the same time, the theory of these polynomials admits wide generalizations. By using the Rodrigues formula for the Jacobi, Laguerre and Hermite polynomials we can come to integral representations for other special functions of mathematical physics, for example, hypergeometric functions and Bessel functions [N16, N18]. On the other hand, a construction scheme for the theory of these polynomials can naturally be generalized to classical orthogonal polynomials of a discrete variable. In view of this in Chap. 1 we shall give in a coherent way a brief description of some basic facts of the theory of classical orthogonal polynomials.