## Lecture by Mourad Ismail on March 16, 2009

You are kindly invited to attend the following lecture by
prof. Mourad Ismail
on March 16, 2009 at the KdV Institute, University of Amsterdam.
Speaker:
Mourad E.H. Ismail (University of Central Florida, Orlando and
King Saud University, Riyadh)

Title:
*Orthogonal polynomials, discriminants, and electrostatic
equilibrium problems*

Date and time:
Monday March 16, 2009, 16.00-17.00 hour

Location:
Korteweg-de Vries Institute, University of Amsterdam,
Euclides building,
Plantage Muidergracht 24, Amsterdam, room P0.18

Further information:
Tom Koornwinder

#### Abstract

Stieltjes and Hilbert derived closed form expressions for discriminants of
Jacobi polynomials. Stieltjes studied the electrostatic equilibrium
problem of *n*-unit charged particles restricted to
(–1,1) under the external field of charges (α+1)/2 and
(β+1)/2
at ∓1. The potential is a logarithmic potential. Stieljes showed that
the equilibrium position of the particle is at the zeros of the Jacobi
polynomial *P*_{n}^{(α,β)}(x).
We discuss the recent developments on
this problem, its extension to general orthogonal polynomials and the role
discriminants play in the solution of the problem. This includes deriving
first order raising and
lowering operators and second order differential
equations for general orthogonal polynomials. Expressions for
discriminants of general orthogonal polynomials are also given. Finally
generalization of discriminants are given and some applications will be
briefly mentioned.
#### Further lecture in Nijmegen

Prof. Ismail will also talk on Wednesday March 18, 2009, 11.00-12.00 hour
in the
general math colloquium of Radboud Universiteit Nijmegen on
*Freud weights and their q-analogues*.

to Tom Koornwinder's home page