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

被引：43

作者：

Marcellan, F.

Martinez-Finkelshtein, A.

Martinez-Gonzalez, P.

机构：

[1] Univ Carlos III Madrid, Escuela Politecn Super, Dept Matemat, Laganes Madrid 28911, Spain

[2] Univ Almeris, Dept Estadist & Matemat Aplicada, La Canada De San Urbano 04120, Almeria, Spain

[3] Univ Granada, Inst Carlos Fis Teor & Computac 1, E-18071 Granada, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2007年 / 207卷 / 02期

关键词：

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

D O I：

10.1016/j.cam.2006.10.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：258 / 272

页数：15