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Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables

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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.

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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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Authors and Affiliations

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

    Francisco Marcellán

  2. Departamento de Matemáticas, Universidad Carlos III de Madrid, 28911, Leganés, Spain

    Misael Marriaga

  3. IEMath—Math. Institute and Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, 18071, Granada, Spain

    Teresa E. Pérez & Miguel A. Piñar

Authors
  1. Francisco Marcellán
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  2. Misael Marriaga
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  3. Teresa E. Pérez
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  4. Miguel A. Piñar
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Corresponding author

Correspondence to Teresa E. Pérez.

Additional information

The work of Francisco Marcellán and Misael Marriaga was partially supported by MINECO of Spain, grant MTM2015-65888-C4-2-P. The work of Teresa E. Pérez and Miguel Piñar was partially supported by MINECO of Spain through the grant MTM2014-53171-P, and Junta de Andalucía FQM-384 and P11-FQM-7276.

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Marcellán, F., Marriaga, M., Pérez, T.E. et al. Matrix Pearson Equations Satisfied by Koornwinder Weights in Two Variables. Acta Appl Math 153, 81–100 (2018). https://doi.org/10.1007/s10440-017-0121-6

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  • DOI: https://doi.org/10.1007/s10440-017-0121-6

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