Asymptotic behavior of orthogonal polynomials. Singular critical case

Our goal is to find an asymptotic behavior as n→∞ of the orthogonal polynomials Pn(z) defined by Jacobi recurrence coefficients an (off-diagonal terms) and bn (diagonal terms). We consider the case an→∞, bn→∞ in such a way that ∑an−1

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Bibliographic Details
Published in:Journal of approximation theory 2021-02, Vol.262, p.105506, Article 105506
Main Author: Yafaev, D.R.
Format: Article
Language:English
Subjects:
Carleman condition
Classical Analysis and ODEs
Difference equations
Increasing Jacobi coefficients
Jost solutions
Mathematics
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Summary:Our goal is to find an asymptotic behavior as n→∞ of the orthogonal polynomials Pn(z) defined by Jacobi recurrence coefficients an (off-diagonal terms) and bn (diagonal terms). We consider the case an→∞, bn→∞ in such a way that ∑an−1
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2020.105506