Some Linear Functionals Having Classical Orthogonal Polynomials as Moments

Abstract

In this paper, we deal with some linear functionals on the vector space of polynomials whose moments are, in certain normalization, classical orthogonal polynomials (Hermite, Laguerre and Gegenbauer). We show that these linear functionals are semiclassical of class, at most, three. We give the coefficients in the three-term recurrence relations that the corresponding monic orthogonal polynomial sequences satisfy.