Electrostatic models for zeros of polynomials: Old,new, and some open problems |
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| Authors: | F. Marcellá n,A. Martí nez-Finkelshtein,P. Martí nez-Gonzá lez |
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| Affiliation: | 1. Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III, Avenida de la Universidad, 30, 28911 Leganés-Madrid, Spain;2. Departamento de Estadística y Matemática Aplicada, Universidad de Almería, La Cañada, 04120 Almería, Spain;3. Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain |
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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. |
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| Keywords: | Primary, 30C15 secondary, 34C10 33C45 42C05 82B23 |
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