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http://acervodigital.unesp.br/handle/11449/21753
- Title:
- Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials
- Universidade Estadual Paulista (UNESP)
- Univ Carlos III
- Universidade Estadual de Campinas (UNICAMP)
- 0022-247X
- Direccion General de Investigacion, Ministerio de Educacion y Ciência of Spain
- Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
- Comunidad de Madrid-Universidad Carlos III de Madrid
- Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
- Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
- Direccion General de Investigacion, Ministerio de Educacion y Ciência of Spain: MTM06-13000-C03-02
- CAPES: DGU 160/08
- Comunidad de Madrid-Universidad Carlos III de Madrid: CCG07-UC3M/ESP-3339
- CNPq: 304830/2006-2
- FAPESP: 03/01874-2
- FAPESP: 07/02854-6
- 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 B.V. All rights reserved.
- 1-Aug-2010
- Journal of Mathematical Analysis and Applications. San Diego: Academic Press Inc. Elsevier B.V., v. 368, n. 1, p. 80-89, 2010.
- 80-89
- Academic Press Inc. Elsevier B.V.
- Orthogonal polynomials
- Laguerre polynomial
- Sobolev-type orthogonal polynomials
- Zeros
- Monotonicity
- Asymptotic
- http://dx.doi.org/10.1016/j.jmaa.2010.02.038
- Acesso restrito
- outro
- http://repositorio.unesp.br/handle/11449/21753
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