Characterizations of generalized Hermite and sieved ultraspherical polynomials
Abstract
A new characterization of the generalized Hermite polynomials and of the orthogonal polynomials with respect to the maesure $x^\g (1x^2)^{\a1/2}dx$ 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 generalized 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1994
 arXiv:
 arXiv:math/9406221
 Bibcode:
 1994math......6221D
 Keywords:

 Mathematics  Classical Analysis and ODEs