Classical Orthogonal Polynomials - Characterizations of Classical Orthogonal Polynomials

Characterizations of Classical Orthogonal Polynomials

There are several conditions that single out the classical orthogonal polynomials from the others.

The first condition was found by Sonine (and later by Hahn), who showed that (up to linear changes of variable) the classical orthogonal polynomials are the only ones such that their derivatives are also orthogonal polynomials.

Bochner characterized classical orthogonal polynomials in terms of their recurrence relations.

Tricomi characterized classical orthogonal polynmials as those that have a certain analogue of the Rodrigues formula.