Acta Applicandae Mathematicae

, Volume 153, Issue 1, pp 81–100 | Cite as

Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables

  • Francisco Marcellán
  • Misael Marriaga
  • Teresa E. Pérez
  • Miguel A. Piñar
Article

Abstract

We consider Koornwinder’s method for constructing orthogonal polynomials in two variables from orthogonal polynomials in one variable. If semiclassical orthogonal polynomials in one variable are used, then Koornwinder’s construction generates semiclassical orthogonal polynomials in two variables. We consider two methods for deducing matrix Pearson equations for weight functions associated with these polynomials, and consequently, we deduce the second order linear partial differential operators for classical Koornwinder polynomials.

Keywords

Orthogonal polynomials in two variables Koornwinder weights Partial differential equations Matrix Pearson equations 

Mathematics Subject Classification (2010)

42C05 33C50 

Notes

Acknowledgements

The authors thank to the anonymous referees for their careful revision of the manuscript. Their comments and suggestions contributed to improve the presentation.

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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  • Francisco Marcellán
    • 1
  • Misael Marriaga
    • 2
  • Teresa E. Pérez
    • 3
  • Miguel A. Piñar
    • 3
  1. 1.Instituto de Ciencias Matemáticas (ICMAT) and Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganésSpain
  3. 3.IEMath—Math. Institute and Departamento de Matemática Aplicada, Facultad de CienciasUniversidad de GranadaGranadaSpain

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