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Zbl 0859.41025
Rui, Bo; Wong, R.
Asymptotic behavior of the Pollaczek polynomials and their zeros. (English)
[J] Stud. Appl. Math. 96, No.3, 307-338 (1996). ISSN 0022-2526; ISSN 1467-9590/e

The Pollaczek polynomials are represented by means of the Cauchy integral that follows from the generating function. The saddle point method is used to derive an expansion in terms of Airy functions. The paper gives a detailed discussion of the complicated saddle point analysis, the conformal mapping of the phase function to a cubic polynomial, the leading terms of the expansion, and the local (non-uniform) behavior that can be derived from the Airy-type expansion. In the discussion on the zeros of the polynomials the authors compare the approximation for the zeros with an earlier result obtained by {\it M. E. H. Ismail} [SIAM J. Math. Anal. 25, No. 2, 462-473 (1994; Zbl 0805.33005)], and they give corrections to this result.
[N.M.Temme (Amsterdam)]

MSC 2000:: *41A60 Asymptotic problems in approximation
33C45 Orthogonal polynomials and functions of hypergeometric type

Keywords: uniform asymptotic expansion; zeros of high degree polynomials; Pollaczek polynomials

Citations: Zbl 0805.33005

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