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Characterization of q-Dunkl-classical symmetric orthogonal q-polynomials

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Abstract

In this paper, we show that, up to a dilatation, the \(q^2\)-analogue of generalized Hermite and \(q^2\)-analogue of generalized Gegenbauer polynomials are the only q-Dunkl-classical symmetric orthogonal polynomials.

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Acknowledgements

The author would like to thank the referees for their corrections and many valuable suggestions.

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Authors and Affiliations

  1. Department of Electromechanics, Higher Institute of Industrial Systems of Gabes, Gabes University, Street Salah Eddine Elayoubi, 6033, Gabes, Tunisia

    Baghdadi Aloui

  2. Department of Mathematics, Faculty of Sciences of Gabes, Gabes University, Street Erriadh, 6072, Gabes, Tunisia

    Jihad Souissi

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  1. Baghdadi Aloui
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  2. Jihad Souissi
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Correspondence to Jihad Souissi.

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Aloui, B., Souissi, J. Characterization of q-Dunkl-classical symmetric orthogonal q-polynomials. Ramanujan J 57, 1355–1365 (2022). https://doi.org/10.1007/s11139-021-00425-8

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