Constructive Approximation

, Volume 17, Issue 1, pp 59–90 | Cite as

On the Asymptotics of the Meixner—Pollaczek Polynomials and Their Zeros

  • X. Li
  • R. Wong
Article

Abstract.

An infinite asymptotic expansion is derived for the Meixner—Pollaczek polynomials M n (nα;δ, η) as n→∞ , which holds uniformly for -M≤α≤ M , where M can be any positive number. This expansion involves the parabolic cylinder function and its derivative. If α n, s denotes the s th zero of M n (nα;δ, η) , counted from the right, and if α˜ n,s denotes its s th zero counted from the left, then for each fixed s , three-term asymptotic approximations are obtained for both α n,s and α˜ n,s as n→∞ .

Key words. Meixner—Pollaczek polynomials, Uniform asymptotic expansions, Parabolic cylinder functions, Zeros. AMS Classification. Primary 41A60, 33C45. 

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Copyright information

© Springer-Verlag New York Inc. 2000

Authors and Affiliations

  • X. Li
    • 1
  • R. Wong
    • 2
  1. 1.Department of Basic Science Beijing Institute of Printing Beijing ChinaCN
  2. 2.Department of Mathematics City University of Hong Kong Tat Chee Avenue Kowloon Hong KongHK

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