Asymptotics for Laguerre polynomials with large order and parameters
Abbreviated Journal Title
J. Approx. Theory
Riemann-Hilbert problem; Laguerre polynomial; Strong asymptotics; RIEMANN-HILBERT PROBLEMS; ORTHOGONAL POLYNOMIALS; HERMITE-POLYNOMIALS; EXPONENTIAL WEIGHTS; GLOBAL ASYMPTOTICS; EXPANSIONS; RESPECT; JACOBI; Mathematics
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 of Approximation Theory
"Asymptotics for Laguerre polynomials with large order and parameters" (2015). Faculty Bibliography 2010s. 6484.