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

2005/12/13 by Francisco Marcellán, Andrei Martı́nez-Finkelshtein, Marcellan, F. +3 · 1 citation
Mathematics · #26C10 #30C15 #31A05 #33C45 #33C47 #42C05 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.math/0512293

openalex publication_date 2005/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• A differential equation for orthogonal polynomials

Cited by

• Optimal polynomial approximants and orthogonal polynomials on the unit circle. An electrostatic approach

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