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

A. Garrido, J. Arvesú, and F. Marcellán

### 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 for the distribution of zeros of the corresponding orthogonal polynomials.

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### Key words

Freud weights, orthogonal polynomials, zeros, potential theory, semiclassical linear functional.

### AMS subject classifications

Primary 33C45, secondary 42C05.