An electrostatics model for zeros of general orthogonal polynomials

Mourad E.H. Ismail

Vol. 193 (2000), No. 2, 355–369

DOI: 10.2140/pjm.2000.193.355

Abstract

We prove that the zeros of general orthogonal polynomials, subject to certain integrability conditions on their weight functions determine the equilibrium position of movable n unit charges in an external field determined by the weight function. We compute the total energy of the system in terms of the recursion coefficients of the orthonormal polynomials and study its limiting behavior as the number of particles tends to infinity in the case of Freud exponential weights.

Milestones

Received: 24 March 1998

Published: 1 April 2000