The asymptotic zero distribution of multiple orthogonal polynomials associated with Macdonald functions

JOURNAL OF APPROXIMATION THEORY

卷:163

Article

Zhang, Lun¹  Roman, Pablo¹ 

[1] Katholieke Univ Leuven, Dept Math, B-3001 Louvain, Belgium

关键词: Asymptotic zero distribution;    Multiple orthogonal polynomials;    Recurrence relation;    Vector equilibrium problem;   

DOI  :  10.1016/j.jat.2010.08.003

来源: Elsevier

【 摘 要 】

We study the asymptotic zero distribution of type II multiple orthogonal polynomials associated with two Macdonald functions (modified Bessel functions of the second kind). On the basis of the four-term recurrence relation, it is shown that, after proper scaling, the sequence of normalized zero counting measures converges weakly to the first component of a vector of two measures which satisfies a vector equilibrium problem with two external fields. We also give the explicit formula for the equilibrium vector in terms of solutions of an algebraic equation. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free