Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607013 | Journal of Approximation Theory | 2015 | 18 Pages |
Abstract
In this paper, we consider the Hankel determinants associated with the singularly perturbed Laguerre weight w(x)=xαe−x−t/xw(x)=xαe−x−t/x, x∈(0,∞)x∈(0,∞), t>0t>0 and α>0α>0. When the matrix size n→∞n→∞, we obtain an asymptotic formula for the Hankel determinants, valid uniformly for t∈(0,d]t∈(0,d], d>0d>0 fixed. A particular Painlevé III transcendent is involved in the approximation, as well as in the large-nn asymptotics of the leading coefficients and recurrence coefficients for the corresponding perturbed Laguerre polynomials. The derivation is based on the asymptotic results in an earlier paper of the authors, obtained by using the Deift–Zhou nonlinear steepest descent method.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Shuai-Xia Xu, Dan Dai, Yu-Qiu Zhao,