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Classical orthogonal polynomials in two variables: a matrix approach

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Abstract

Classical orthogonal polynomials in two variables are defined as the orthogonal polynomials associated to a two-variable moment functional satisfying a matrix analogue of the Pearson differential equation. Furthermore, we characterize classical orthogonal polynomials in two variables as the polynomial solutions of a matrix second order partial differential equation.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Granada, Granada, Spain

    Lidia Fernández

  2. Universidad de Granada, Departamento de Matemática Aplicada, and Instituto Carlos I de Física Teórica y Computacional, Granada, Spain

    Teresa E. Pérez & Miguel A. Piñar

Authors
  1. Lidia Fernández
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  2. Teresa E. Pérez
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  3. Miguel A. Piñar
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Corresponding author

Correspondence to Lidia Fernández.

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AMS subject classification

42C05, 33C50

Partially supported by Ministerio de Ciencia y Tecnología (MCYT) of Spain and by the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02, Junta de Andalucía, G.I. FQM 0229 and INTAS Project 2000-272.

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Fernández, L., Pérez, T.E. & Piñar, M.A. Classical orthogonal polynomials in two variables: a matrix approach. Numer Algor 39, 131–142 (2005). https://doi.org/10.1007/s11075-004-3625-x

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  • DOI: https://doi.org/10.1007/s11075-004-3625-x

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