Electrostatic models for zeros of polynomials: Old, new, and some open problems

Authors:
F. Marcellán;A. Martínez-Finkelshtein;P. Martínez-González
Affiliations:
Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Avenida de la Universidad, 30, 28911 Leganés-Madrid, Spain;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada, 04120 Almería, Spain and Instituto Carlos I de Física Teórica y Computacion ...;Departamento de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada, 04120 Almería, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some well-known families of polynomials, and the interplay between these models and the asymptotic distribution of their zeros when the degree of the polynomials tends to infinity. The leading role is played by the differential equation satisfied by these polynomials. Some new developments, applications and open problems are presented.