Zero Asymptotics of Laurent Orthogonal Polynomials

✍ Scribed by Manuel Bello Hernández; Andrei Martı́nez Finkelshtein

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 564 KB
• Volume: 85
• Category: Article
• ISSN: 0021-9045
• DOI: 10.1006/jath.1996.0046

✦ Synopsis

Let [h n (z)] be the sequence of polynomials, satisfying

where * n # [0, 2n], n # N. For a wide class of weights d(x) and under the assumption lim n Ä * n Â(2n)=% # [0, 1], two descriptions of the zero asymptotics of [h n (z)] are obtained. Furthermore, their analogues for polynomials orthogonal on [&1, 1] with respect to varying weights are considered. These results continue the study begun in [3].

1996 Academic Press, Inc.

and starting from its asymptotic expansion at the endpoints of the convex hull of S(), we can construct the so-called two-point Pade approximants:

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