Title: The asymptotic behaviour of recurrence coefficients for orthogonal polynomials with varying exponential weights
Authors: Kuijlaars, Arno ×
Tibboel, Pieter #
Issue Date: 2009
Publisher: Elsevier
Series Title: Journal of Computational and Applied Mathematics vol:233 issue:3 pages:775-785
Abstract: We consider orthogonal polynomials {p_{n,N}(x)}_{n=0}^{∞} 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 -> ∞ in powers of 1/n^2 and powers of 1/n, respectively.
ISSN: 0377-0427
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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