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Finite Orthogonal Laurent Polynomials

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The Mathematics of the Uncertain

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 142))

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Abstract

In this work, orthogonal Laurent polynomials on the real line associated with a finite family of classical orthogonal polynomials (the so called Romanovski–Hermite polynomial sequence) are discussed. Their explicit representation, a second order linear differential equation they satisfy as well as their orthogonality relations are obtained. The connection with a strong Stieltjes moment problem is discussed. The strong Gaussian quadrature formulae are also given. For such a family of orthogonal Laurent polynomials, a comparison with the classical Gaussian quadrature formulae is illustrated with some examples.

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Acknowledgements

The work of the first author (FM) has been supported by Dirección General de Investigación Científica y Técnica, Ministerio de Economía, Industria y Competitividad of Spain, grant MTM2015-65888-C4-2-P.

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Authors and Affiliations

  1. Instituto de Ciencias Matemáticas (ICMAT) and Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain

    Francisco Marcellán

  2. Department of Mathematics, Indian Institute of Technology, Roorkee 247 667, Uttarkhand, India

    Anbhu Swaminathan

Authors
  1. Francisco Marcellán
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  2. Anbhu Swaminathan
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Corresponding author

Correspondence to Francisco Marcellán .

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Editors and Affiliations

  1. Liberbank, Oviedo, Spain

    Eduardo Gil

  2. Viajes El Corte Inglés, Oviedo, Spain

    Eva Gil

  3. Funl Media, Oxford, United Kingdom

    Juan Gil

  4. Departamento de Estadística e Investigación Operativa y Didáctica de la Matemática, Facultad de Ciencias, Universidad de Oviedo, Oviedo, Spain

    María Ángeles Gil

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Marcellán, F., Swaminathan, A. (2018). Finite Orthogonal Laurent Polynomials. In: Gil, E., Gil, E., Gil, J., Gil, M. (eds) The Mathematics of the Uncertain. Studies in Systems, Decision and Control, vol 142. Springer, Cham. https://doi.org/10.1007/978-3-319-73848-2_79

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  • DOI: https://doi.org/10.1007/978-3-319-73848-2_79

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73847-5

  • Online ISBN: 978-3-319-73848-2

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