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Rodrigues formula and recurrence coefficients for non-symmetric Dunkl-classical orthogonal polynomials

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Abstract

In this paper, we establish a distributional Rodrigues formula for non-symmetric Dunkl-classical orthogonal polynomial sequences. Then, we use this formula to determine, explicitly, the coefficients in the three-term recurrence relation that non-symmetric Dunkl-classical polynomial sequences satisfy.

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Acknowledgements

The authors are very grateful to the referees for their constructive and valuable comments. Their suggestions and remarks have contributed to improve substantially the presentation of the manuscript.

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Authors and Affiliations

  1. Department of Mathematics, College of Sciences, Gabès University, Gabès, Tunisia

    B. Bouras & Y. Habbachi

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

    F. Marcellán

Authors
  1. B. Bouras
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  2. Y. Habbachi
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  3. F. Marcellán
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Correspondence to Y. Habbachi.

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The work of the third author (FM) has been supported by Agencia Estatal de Investigación of Spain, Grant PGC2018-096504-B-C33.

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Bouras, B., Habbachi, Y. & Marcellán, F. Rodrigues formula and recurrence coefficients for non-symmetric Dunkl-classical orthogonal polynomials. Ramanujan J 56, 451–466 (2021). https://doi.org/10.1007/s11139-021-00419-6

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  • DOI: https://doi.org/10.1007/s11139-021-00419-6

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