The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:233

Article; Proceedings Paper

Kuijlaars, A. B. J.¹  Tibboel, P. M. J.¹ 

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

关键词: Riemann-Hilbert problems;    Recurrence coefficients;    Orthogonal polynomials;    Steepest descent analysis;   

DOI  :  10.1016/j.cam.2009.02.090

来源: Elsevier

【 摘 要 】

We consider orthogonal polynomials {p(n,N)(x)}(n=0)(infinity) on the real line with respect to a weight w(x) = e(-NV(x)) and in particular the asymptotic behaviour of the coefficients a(n,N) and b(n,N) in the three-term recurrence x pi(n,N)(x) = pi(n+1,N)(x) + b(n,N) pi(n,N)(x) + a(n,N) pi(n-1,N)(x). For one-cut regular V we show, using the Deift-Zhou method of steepest descent for Riemann-Hilbert problems, that the diagonal recurrence coefficients a(n,n) and b(n,n) have asymptotic expansions as n -> infinity in powers of 1/n(2) and powers of 1/n, respectively. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free