Turning Point Theory and Asymptotics, Old and
New Problems Involving Orthogonal Polynomials
Dr. Mourad Ismail
Department of Mathematics
University of Central Florida
ABSTRACT: We discuss the asymptotics of classical and q-orthogonal polynomials
around the largest zero and in the oscillatory domain. We show how this is an instant
of the Green-Liouvile or WKB asymptotic method. A crucial step is the understanding
of the turning point theory of ODE's. We indicate how a similar theory works for
q-difference equations and discuss universality.
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