Original Article

Global Asymptotics for Meixner-Pollaczek Polynomials with a Varying Parameter

  1. Jun Wang1,
  2. Weiyuan Qiu2,
  3. R. Wong3,*

Article first published online: 13 FEB 2013

DOI: 10.1111/j.1467-9590.2012.00570.x

Issue

Studies in Applied Mathematics

Studies in Applied Mathematics

Volume 130, Issue 4, pages 345–392, May 2013

Additional Information

How to Cite

Wang, J., Qiu, W. and Wong, R. (2013), Global Asymptotics for Meixner-Pollaczek Polynomials with a Varying Parameter. Studies in Applied Mathematics, 130: 345–392. doi: 10.1111/j.1467-9590.2012.00570.x

Author Information

  1. 1

    Fudan University

  2. 2

    Fudan University

  3. 3

    City University of Hong Kong

*Address for correspondence: R. Wong, Department of Mathematics, City University of Hong Kong, Hong Kong; e-mail: mawong@cityu.edu.hk

Publication History

  1. Issue published online: 17 APR 2013
  2. Article first published online: 13 FEB 2013
  3. Manuscript Received: 20 JUL 2012

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In this paper, we study the uniform asymptotics of the Meixner-Pollaczek polynomials inline image with varying parameter inline image as inline image, where A > 0 is a constant. Two asymptotic expansions are obtained, which hold uniformly for z in two overlapping regions which together cover the whole complex plane. One involves parabolic cylinder functions, and the other is in terms of elementary functions only. Our approach is based on the steepest descent method for oscillatory Riemann-Hilbert problems first introduced by Deift and Zhou [1].

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