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Transactions of the Moscow Mathematical Society

ISSN 1547-738X(online) ISSN 0077-1554(print)

 

 

Asymptotic expansions for polynomials orthogonal with respect to a complex non-constant weight function


Authors: A. Aptekarev and R. Khabibullin
Translated by: Michael Grinfeld
Original publication: Trudy Moskovskogo Matematicheskogo Obshchestva, tom 68 (2007).
Journal: Trans. Moscow Math. Soc. 2007, 1-37
MSC (2000): Primary 42C05
DOI: https://doi.org/10.1090/S0077-1554-07-00167-7
Published electronically: November 15, 2007
MathSciNet review: 2429265
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a sequence of polynomials that are orthogonal with respect to a complex analytic weight function which depends on the index $ n$ of the polynomial. For such polynomials we obtain an asymptotic expansion in $ 1/n$. As an example, we present the asymptotic expansion for Laguerre polynomials with a weight that depends on the index of the polynomial.


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Additional Information

A. Aptekarev
Affiliation: The M. V. Keldysh Applied Mathematics Institute, Russian Academy of Sciences, Miusskaya Sq. 4, Moscow 125047, Russia
Email: aptekaa@keldysh.ru

R. Khabibullin
Affiliation: The M. V. Keldysh Applied Mathematics Institute, Russian Academy of Sciences, Miusskaya Sq. 4, Moscow 125047, Russia

DOI: https://doi.org/10.1090/S0077-1554-07-00167-7
Published electronically: November 15, 2007
Additional Notes: This work has been supported by the Russian Fund for Fundamental Research (grant No. 05–01–00522), the Support of Leading Scientific Institutions in the RF Programme (grant No. NSh-1551.2003.1), The Mathematical Sciences Department of the Russian Academy of Sciences (programme no. 1) and the INTAS fund (grant No. 03-516637).
Article copyright: © Copyright 2007 American Mathematical Society