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


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 Pn(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