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Type: Artigo de periódico
Title: Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials
Author: Dimitrov, DK
Marcellan, F
Rafaeli, FR
Abstract: Denote by x(n,k)(M,N)(alpha), k = 1, ..., n, the zeros of the Laguerre-Sobolev-type polynomials L(n)((alpha, M, N))(x) orthogonal with respect to the inner product < p, q > = 1/Gamma(alpha + 1) integral(infinity)(0)p(x)q(x)x(alpha)e(-x) dx + Mp(0)q(0) + Np'(0)q'(0), where alpha > -1, M >= 0 and N >= 0. We prove that x(n,k)(M,N)(alpha) interlace with the zeros of Laguerre orthogonal polynomials L(n)((alpha))(x) and establish monotonicity with respect to the parameters M and N of x(n,k)(M,0)(alpha) and x(n,k)(0,N)(alpha). Moreover, we find N(0) such that x(n,n)(M,N)(alpha) < 0 for all N > N(0), where x(n,n)(M,N)(alpha) is the smallest zero of L(n)((alpha, M, N))(x). Further, we present monotonicity and asymptotic relations of certain functions involving x(n,k)(M,0)(alpha) and x(n,k)(0,N)(alpha). (C) 2010 Elsevier Inc. All rights reserved.
Subject: Orthogonal polynomials
Laguerre polynomials
Sobolev-type orthogonal polynomials
Country: EUA
Editor: Academic Press Inc Elsevier Science
Rights: fechado
Identifier DOI: 10.1016/j.jmaa.2010.02.038
Date Issue: 2010
Appears in Collections:Unicamp - Artigos e Outros Documentos

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