Electrostatic models for zeros of polynomials: old, new, and some open problems
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2007Abstract
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.
Palabra/s clave
Ecuación diferencial de segundo orden
Polinomios ortogonales
Ceros
Asíntotas
Modelo elestrostático
Potencial logarítmico
Second order differential equation
Orthogonal polynomials
Zeros
Asymptotics
Electrostatic model
Logarithmic potential