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

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....

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2007-10, Vol.207 (2), p.258-272
Main Authors: Marcellán, F., Martínez-Finkelshtein, A., Martínez-González, P.
Format: Article
Language:English
Subjects:
Asymptotics
Electrostatic model
Exact sciences and technology
Fourier analysis
Logarithmic potential
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equations
Orthogonal polynomials
Sciences and techniques of general use
Second order differential equation
Special functions
Zeros
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Summary: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.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2006.10.020