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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Zeros of varying Laguerre–Krall orthogonal polynomials
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by Laura Castaño–García and Juan J. Moreno–Balcázar PDF
Proc. Amer. Math. Soc. 141 (2013), 2051-2060 Request permission

Abstract:

In this paper we introduce a sequence of varying orthogonal polynomials related to a Laguerre weight where this absolutely continuous measure is perturbed by a sequence of nonnegative masses located at the origin. The main objective is to obtain asymptotic relations between the zeros of these polynomials and the zeros of the Bessel functions of the first kind (or linear combinations of them). This is done through Mehler–Heine type formulas. With these relations we can easily compute asymptotically the zeros of these polynomials. We show some numerical experiments.
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Additional Information
  • Laura Castaño–García
  • Affiliation: Departamento de Estadística y Matemática Aplicada, Universidad de Almería, 04120 Almería, Spain
  • Email: lcastano@ual.es
  • Juan J. Moreno–Balcázar
  • Affiliation: Departamento de Estadística y Matemática Aplicada, Universidad de Almería, 04120 Almería, Spain
  • Email: balcazar@ual.es
  • Received by editor(s): June 15, 2011
  • Received by editor(s) in revised form: October 2, 2011
  • Published electronically: January 17, 2013
  • Additional Notes: This research was supported by MICINN of Spain under grants MTM2008-06689-C02-01 and MTM2011-28952-C02-01, and Junta de Andalucía (FQM229 and P09–FQM–4643).
  • Communicated by: Walter Van Assche
  • © Copyright 2013 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2051-2060
  • MSC (2010): Primary 33C47; Secondary 42C05
  • DOI: https://doi.org/10.1090/S0002-9939-2013-11495-4
  • MathSciNet review: 3034430