کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4607013 1631418 2015 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Painlevé III asymptotics of Hankel determinants for a singularly perturbed Laguerre weight
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Approximation Theory - Volume 192, April 2015, Pages 1–18
نویسندگان
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