The distribution of zeros of general q-polynomials

Abstract

A general system of q-orthogonal polynomials is de ned by means of its three-term recurrence relation. This system encompasses many of the known families of q-polynomials, among them the q-analog of the classical orthogonal polynomials. The asymptotic density of zeros of the system is shown to be a simple and compact expression of the parameters which characterize the asymptotic behavior of the coe cients of the recurrence relation. This result is applied to speci c classes of polynomials known by the names q-Hahn, q-Kravchuk, q-Racah,q-Askey & Wilson, Al Salam-Carlitz and the celebrated q-little and q-big Jacobi.