Volume 19, pp. 37-47, 2005.

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.

ETNA articles which cite this article

Vol. 26 (2007), pp. 439-452 Joris Van Deun: Electrostatics and ghost poles in near best fixed pole rational interpolation
Vol. 44 (2015), pp. 271-280 Kenier Castillo and Fernando R. Rafaeli: On the discrete extension of Markov's theorem on monotonicity of zeros

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