The Meixner--Pollaczek polynomials and a system of orthogonal polynomials in a strip
type: Item
instance of: scholarly article
title: The Meixner--Pollaczek polynomials and a system of orthogonal polynomials in a strip
zbMATH Open document ID: 1053.33004
author: Tsehaye K. Araaya
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-10T00:00:00Z
review text: Two systems of polynomials \(\{\tau_n\}\) and \(\{\sigma_n\}\) which satisfy the recursion relations \[ \tau_{n+1}(z)=z\tau_n(z)-n^2\tau_{n-1}(z), \quad n\geq0, \qquad \tau_{-1}=0, \;\tau_0=1 \] and \[ \sigma_{n+1}(z)=z\sigma_n(z)-n(n-1)\sigma_{n-1}(z), \quad n\geq0, \qquad \sigma_{-1}=0, \;\sigma_0=1, \] respectively, are under consideration in the present paper. The first system is known to be a special case of the symmetric Meixner-Pollaczek polynomials orthogonal with respect to the weight function \(w=1/2\cosh(\pi x/2)\). The second one turns out to form an orthogonal basis in the Hilbert space of functions analytic in a certain strip of the complex plane. The author finds some simple operators that connect the systems with each other which makes it possible to study the asymptotic behavior of the second system.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 2085567
zbMATH Keywords: Meixner-Pollaczek polynomials
zbMATH Keywords: orthogonal polynomilas
zbMATH Keywords: Poisson kernel
zbMATH Keywords: generating function
reviewed by: Leonid Golinskii
MaRDI profile type: Publication
full work available at URL: j.cam.2004.01.039
OpenAlex ID: W1975153112
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DOI: 10.1016/J.CAM.2004.01.039
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description: scientific article; zbMATH DE number 2085567