Asymptotics For Laguerre Polynomials With Large Order And Parameters

Keywords

Laguerre polynomial; Riemann-Hilbert problem; Strong asymptotics

Abstract

We study the asymptotic behavior of Laguerre polynomials Ln(αn)(z) as n→∞, where αn/n has a finite positive limit or the limit is +∞. 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.

Publication Date

5-1-2015

Publication Title

Journal of Approximation Theory

Volume

193

Number of Pages

4-19

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jat.2014.03.009

Socpus ID

84896692304 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84896692304

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