Global asymptotics of hermite polynomials via Riemann-Hilbert approach

R. Wong; L. Zhang

doi:10.3934/dcdsb.2007.7.661

Global asymptotics of hermite polynomials via Riemann-Hilbert approach

R. Wong
, L. Zhang

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

14 Citations (Scopus)

Abstract

In this paper, we study the asymptotic behavior of the Hermite polynomials H_n((2n + 1)^1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.

Original language	English
Pages (from-to)	661-682
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/dcdsb.2007.7.661
Publication status	Published - May 2007

Research Keywords

Airy functions
Global asymptotics
Hermite polynomials
Riemann-Hilbert problems

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abstract = "In this paper, we study the asymptotic behavior of the Hermite polynomials Hn((2n + 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.",

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AU - Wong, R.

AU - Zhang, L.

PY - 2007/5

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N2 - In this paper, we study the asymptotic behavior of the Hermite polynomials Hn((2n + 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.

AB - In this paper, we study the asymptotic behavior of the Hermite polynomials Hn((2n + 1)1/2z) as n → ∞. A globally uniform asymptotic expansion is obtained for z in an unbounded region containing the right half-plane Re z ≥ 0. A corresponding expansion can also be given for z in the left half-plane by using the symmetry property of the Hermite polynomials. Our approach is based on the steepest-descent method for Riemann-Hilbert problems introduced by Deift and Zhou.

KW - Airy functions

KW - Global asymptotics

KW - Hermite polynomials

KW - Riemann-Hilbert problems

UR - https://www.scopus.com/pages/publications/34250872302

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-34250872302&origin=recordpage

U2 - 10.3934/dcdsb.2007.7.661

DO - 10.3934/dcdsb.2007.7.661

M3 - RGC 21 - Publication in refereed journal

SN - 1531-3492

VL - 7

SP - 661

EP - 682

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 3

ER -

Global asymptotics of hermite polynomials via Riemann-Hilbert approach

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