Abstract and Applied Analysis
Volume 2010 (2010), Article ID 263860, 14 pages
Research Article

On the Complex Zeros of Some Families of Orthogonal Polynomials

Division of Applied Mathematics and Mechanics, Department of Engineering Sciences, University of Patras, 26500 Patras, Greece

Received 8 March 2010; Accepted 6 May 2010

Academic Editor: Roman Šimon Hilscher

Copyright © 2010 Eugenia N. Petropoulou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The complex zeros of the orthogonal Laguerre polynomials Ln(a)(x) for a<-n, ultraspherical polynomials Pn(λ)(x) for λ<-n, Jacobi polynomials Pn(a,β)(x) for a<-n, β<-n, a+β<-2(n+1), orthonormal Al-Salam-Carlitz II polynomials Pn(a)(x;q) for a<0, 0<q<1, and q-Laguerre polynomials Ln(a)(x;q) for a<-n, 0<q<1 are studied. Several inequalities regarding the real and imaginary properties of these zeros are given, which help locating their position. Moreover, a few limit relations regarding the asymptotic behavior of these zeros are proved. The method used is a functional analytic one. The obtained results complement and improve previously known results.