CHARACTERIZATION OF CLASSICAL TYPE ORTHOGONAL POLYNOMIALS

Abstract

We characterize the classical type orthogonal polynomials {P(n)(x)}0infinity satisfying a fourth-order differential equation of type [GRAPHICS] where l(i)(x) are polynomials of degree less-than-or-equal-to i and lambda(n) is a constant. They are only the orthogonal polynomials satisfying an orthogonality of the form [tau2, P(m)''P(n)'') + [tau1, P(m)'P(n)'] + [tau0, P(m)P(n)] = 0 for m not-equal n where tau0, tau1, and tau2 are moment functionals.