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On some perturbed q-Laguerre–Hahn orthogonal q-polynomials

Abstract

Our goal is to study the multiplication by a polynomial of a \(H_q\)-Laguerre–Hahn form and its inverse one where \(H_q\) be the q-derivative operator. The class of the obtained form is discussed in detail in the two cases. Some examples in connection with the \(H_{q}\)-semiclassical forms are highlighted.

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Acknowledgements

We would like to thank the referee for valuable review, helpful suggestions and bringing certain references to our attention.

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Correspondence to L. Khériji.

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Jbeli, S., Khériji, L. On some perturbed q-Laguerre–Hahn orthogonal q-polynomials. Period Math Hung (2022). https://doi.org/10.1007/s10998-022-00463-9

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  • DOI: https://doi.org/10.1007/s10998-022-00463-9

Keywords

  • Orthogonal q-polynomials
  • q-derivative operator
  • q-Laguerre–Hahn character
  • Regular form
  • Standard perturbations

Mathematics Subject Classification

  • Primary 33C45
  • Secondary 42C05