An electrostatic interpretation of the zeros of the Freud-type orthogonal polynomials

Abstract

Polynomials orthogonal with respect to a perturbation of the Freud weight function, by the addition of a mass point at zero, are considered. These polynomials, called Freud-type orthogonal polynomials, satisfy a second-order linear differential equation with varying polynomial coefficients. It plays an important role in the electrostatic interpretation of the distributions of zeros of the corresponding orthogonal polynomials.