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Quadrature Rules for L 1-Weighted Norms of Orthogonal Polynomials

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Abstract

In this paper, we obtain L 1-weighted norms of classical orthogonal polynomials (Hermite, Laguerre and Jacobi polynomials) in terms of the zeros of these orthogonal polynomials; these expressions are usually known as quadrature rules. In particular, these new formulae are useful to calculate directly some positive defined integrals as several examples show.

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Authors and Affiliations

  1. Departamento de Matemáticas, Instituto Universitario de, Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009, Zaragoza, Spain

    Luciano Abadias & Pedro J. Miana

  2. Departamento de Matemáticas y Computación, Universidad de La Rioja, 26006, Logroño, Spain

    Natalia Romero

Authors
  1. Luciano Abadias
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  2. Pedro J. Miana
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  3. Natalia Romero
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Corresponding author

Correspondence to Pedro J. Miana.

Additional information

To Laura and Pablo

L. Abadias and P. J. Miana have been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragón, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The third author is supported by Ministerio de Ciencia y Tecnología MTM2011-28636-C02.

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Abadias, L., Miana, P.J. & Romero, N. Quadrature Rules for L 1-Weighted Norms of Orthogonal Polynomials. Mediterr. J. Math. 13, 1291–1306 (2016). https://doi.org/10.1007/s00009-015-0552-0

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  • DOI: https://doi.org/10.1007/s00009-015-0552-0

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