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

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

2005-12-13

arxiv.org/abs/math/0512293v1

Mathematics

Classical Analysis and ODEs

23 pages, 2 figures

Scientific paper

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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