Asymptotics of Meixner polynomials and Christoffel–Darboux kernels

Aptekarev, A.; Tulyakov, D.

doi:10.1090/S0077-1554-2013-00203-4

Asymptotics of Meixner polynomials and Christoffel–Darboux kernels
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by 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.)

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