Moscow Mathematical Society

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

Author(s): A. Aptekarev; 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
Posted: November 15, 2007
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Abstract: We consider a sequence of polynomials that are orthogonal with respect to a complex analytic weight function which depends on the index

of the polynomial. For such polynomials we obtain an asymptotic expansion in

. 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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Retrieve articles in Transactions of the Moscow Mathematical Society with MSC (2000): 42C05

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: 10.1090/S0077-1554-07-00167-7
PII: S 0077-1554(07)00167-7
Posted: 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).
Copyright of article: Copyright 2007, American Mathematical Society

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