Title

Asymptotics for Laguerre polynomials with large order and parameters

Authors

Authors

D. Dai; M. E. H. Ismailb;J. Wang

Comments

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Abbreviated Journal Title

J. Approx. Theory

Keywords

Riemann-Hilbert problem; Laguerre polynomial; Strong asymptotics; RIEMANN-HILBERT PROBLEMS; ORTHOGONAL POLYNOMIALS; HERMITE-POLYNOMIALS; EXPONENTIAL WEIGHTS; GLOBAL ASYMPTOTICS; EXPANSIONS; RESPECT; JACOBI; Mathematics

Abstract

We study the asymptotic behavior of Laguerre polynomials L-n((alpha n)) (z) as n -> infinity, where cznin has a finite positive limit or the limit is +infinity. Applying the Deift Zhou nonlinear steepest descent method for Riemann Hilbert problems, we derive the uniform asymptotics of such polynomials, which improves on the results of Bosbach and Gawronski (1998). In particular, our theorem is useful to obtain the asymptotics of complex Hermite polynomials and related double integrals. (C) 2014 Elsevier Inc. All rights reserved.

Journal Title

Journal of Approximation Theory

Volume

193

Publication Date

1-1-2015

Document Type

Article

Language

English

First Page

4

Last Page

19

WOS Identifier

WOS:000352676400002

ISSN

0021-9045

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