The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights |
| |
Authors: | ABJ Kuijlaars PMJ Tibboel |
| |
Institution: | Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium |
| |
Abstract: | We consider orthogonal polynomials on the real line with respect to a weight and in particular the asymptotic behaviour of the coefficients an,N and bn,N in the three-term recurrence xπn,N(x)=πn+1,N(x)+bn,Nπn,N(x)+an,Nπn−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 an,n and bn,n have asymptotic expansions as n→∞ in powers of 1/n2 and powers of 1/n, respectively. |
| |
Keywords: | Riemann-Hilbert problems Recurrence coefficients Orthogonal polynomials Steepest descent analysis |
本文献已被 ScienceDirect 等数据库收录! |
|