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Asymptotic properties of generalized Laguerre orthogonal polynomials


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Opened Access Asymptotic properties of generalized Laguerre orthogonal polynomials

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Author: Álvarez Nodarse, Renato
Moreno Balcázar, Juan José
Department: Universidad de Sevilla. Departamento de Análisis Matemático
Date: 2004-06
Published in: Indagationes Mathematicae, 15 (2), 151-165.
Document type: Article
Abstract: In the present paper we deal with the polynomials L(α,M,N) n (x) orthogonal with respect to the Sobolev inner product (p, q) = 1 Γ(α+1) Z ∞ 0 p(x)q(x) x α e −x dx + M p(0)q(0) + N p 0 (0)q 0 (0), N,M ≥ 0, α > −1, firstly introduced by Koekoek and Meijer in 1993 and extensively studied in the last years. We present some new asymptotic properties of these polynomials and also a limit relation between the zeros of these polynomials and the zeros of Bessel function Jα(x). The results are illustrated with numerical examples. Also, some general asymptotic formulas for generalizations of these polynomials are conjectured.
Cite: Álvarez Nodarse, R. y Moreno Balcázar, J.J. (2004). Asymptotic properties of generalized Laguerre orthogonal polynomials. Indagationes Mathematicae, 15 (2), 151-165.
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DOI: 10.1016/S0019-3577(04)90012-2

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