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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Monotonicity and asymptotics of zeros of Laguerre-Sobolev-type orthogonal polynomials of higher order derivatives
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by Francisco Marcellán and Fernando R. Rafaeli PDF
Proc. Amer. Math. Soc. 139 (2011), 3929-3936 Request permission


In this paper we analyze the location of the zeros of polynomials orthogonal with respect to the inner product \begin{equation} \langle p,q\rangle = \displaystyle \int _{0}^{\infty }p(x)q(x)x^{\alpha }e^{-x}dx+Np^{(j)}(0)q^{(j)}(0), \end{equation} where $\alpha >-1$, $N\geq 0,$ and $j\in \mathbb {N}.$ In particular, we focus our attention on their interlacing properties with respect to the zeros of Laguerre polynomials as well as on the monotonicity of each individual zero in terms of the mass $N.$ Finally, we give necessary and sufficient conditions in terms of $N$ in order for the least zero of any Laguerre-Sobolev-type orthogonal polynomial to be negative.
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Additional Information
  • Francisco Marcellán
  • Affiliation: Departamento de Matemáticas, Escuela Politécnica Superior, Universidad Carlos III de Madrid, 28911 Leganés, Spain
  • Fernando R. Rafaeli
  • Affiliation: Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, São Paulo, Brazil
  • Address at time of publication: Departamento de Matemática, Estatística e Computação/FCT, Universidade Estadual Paulista-UNESP, 19060-900 Presidente Prudente, São Paulo, Brazil
  • Received by editor(s): November 25, 2009
  • Received by editor(s) in revised form: September 7, 2010
  • Published electronically: March 10, 2011
  • Communicated by: Walter Van Assche
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3929-3936
  • MSC (2010): Primary 42C05; Secondary 33C47
  • DOI:
  • MathSciNet review: 2823039