Global asymptotics of the Meixner polynomials

X. S. Wang; R. Wong

doi:10.1142/9789814656054_0059

Global asymptotics of the Meixner polynomials

X. S. Wang
, R. Wong

Department of Mathematics

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 12 - Chapter in an edited book (Author) › peer-review

Abstract

Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for z on the positive real line by using the steepest descent method for integrals [Constr. Approx. 14 (1998), 113-150]. © 2016 by World Scientific Publishing Co. Ptc. Ltd.

Original language	English
Title of host publication	Selected Works Of Roderick S. C. Wong, The (In 3 Volumes)
Publisher	World Scientific Publishing Co. Pte Ltd
Pages	1337-1357
ISBN (Print)	9789814656054
DOIs	https://doi.org/10.1142/9789814656054_0059
Publication status	Published - 5 Aug 2015

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Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Research Keywords

Airy function
Global asymptotics
Meixner polynomials
Riemann-hilbert problems

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N2 - Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for z on the positive real line by using the steepest descent method for integrals [Constr. Approx. 14 (1998), 113-150]. © 2016 by World Scientific Publishing Co. Ptc. Ltd.

AB - Using the steepest descent method for oscillatory Riemann-Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295-368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for z on the positive real line by using the steepest descent method for integrals [Constr. Approx. 14 (1998), 113-150]. © 2016 by World Scientific Publishing Co. Ptc. Ltd.

KW - Airy function

KW - Global asymptotics

KW - Meixner polynomials

KW - Riemann-hilbert problems

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BT - Selected Works Of Roderick S. C. Wong, The (In 3 Volumes)

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ER -

Global asymptotics of the Meixner polynomials

Abstract

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Research Keywords

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