CHARACTERIZATIONS OF GENERALIZED HERMITE AND SIEVED ULTRASPHERICAL POLYNOMIALS

A new characterization of the generalized Hermite polynomials and of t he orthogonal polynomials with respect to the measure \x\(gamma)(1-x(2 ))(1/2)dx is derived which is based on a ''reversing property'' of the coefficients in the corresponding recurrence formulas and does not us e the representation in terms of Laguerre and Jacobi polynomials. A si milar characterization can be obtained for a generalization of the sie ved ultraspherical polynomials of the first and second kind. These res ults are applied in order to determine the asymptotic limit distributi on for the zeros when the degree and the parameters tend to infinity w ith the same order.