Asymptotics of Meixner polynomials and Christoffel–Darboux kernels
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A. I. Aptekarev and D. N. Tulyakov
Translated by: V. E. Nazaikinskii - Trans. Moscow Math. Soc. 2012, 67-106
- DOI: https://doi.org/10.1090/S0077-1554-2013-00203-4
- Published electronically: January 24, 2013
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Abstract:
We obtain the asymptotics of the classical Meixner polynomials (orthogonal with respect to a discrete measure supported at the nonnegative integer points) and the corresponding reproducing kernels (Christoffel–Darboux kernels) as the number $n$ of the polynomial and the variable $x$ tend to infinity under various relationships between their growth rates. (These asymptotics are known as the Plancherel–Rotach asymptotics.)References
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Bibliographic Information
- A. I. Aptekarev
- Affiliation: Keldysh Institute of Applied Mathematics, 4 Miusskaya pl., 125047 Moscow, Russian Federation
- MR Author ID: 192572
- Email: aptekaa@keldysh.ru
- D. N. Tulyakov
- Affiliation: Keldysh Institute of Applied Mathematics, 4 Miusskaya pl., 125047 Moscow, Russian Federation
- MR Author ID: 632175
- Email: dntulyakov@gmail.com
- Published electronically: January 24, 2013
- Additional Notes: This work was supported in part by RFBR grants no. 11-01-00245 and 11-01-12045-ofi-m and by Program no. 1 of the Branch of Mathematics, Russian Academy of Sciences. The first author was also supported by the Program “Cátedras de Excelencia” of the Universidad Carlos III, Madrid, and Banco Santander. The second author was also supported by RFBR grant No. 10-01-000682.
- © Copyright 2013 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2012, 67-106
- MSC (2010): Primary 33C45; Secondary 60B10
- DOI: https://doi.org/10.1090/S0077-1554-2013-00203-4
- MathSciNet review: 3184968
Dedicated: Dedicated to A. A. Gonchar on the occasion of his eightieth birthday