Asymptotics for Laguerre polynomials with large order and parameters

    Authors

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

    Comments

    Authors: contact us about adding a copy of your work at [email protected]

    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

    Share

    COinS
     

    Accessibility Statement

    This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.