Characterizations of generalized Hermite and sieved ultraspherical polynomials

A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.