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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:207

Article; Proceedings Paper

Marcellan, F. ; Martinez-Finkelshtein, A. ; Martinez-Gonzalez, P.

关键词: second order differential equation;    orthogonal polynomials;    zeros;    asymptotics;    electrostatic model;    logarithmic potential;   

DOI  :  10.1016/j.cam.2006.10.020

来源: Elsevier

【 摘 要 】

We give a survey concerning both very classical and recent results on the electrostatic interpretation of the zeros of some wellknown 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. (C) 2006 Elsevier B.V. All rights reserved.

【 授权许可】

Free