The \(D_{w}\)-Laguerre–Hahn Forms of Class Zero

Abstract

We carry out the complete description of the \(D_{w}\)-Laguerre–Hahn forms of class zero, where \(D_{w}\) is the divided difference operator. Essentially, four canonical cases appear. Some particular cases which refer to well-known orthogonal sequences are exhibited.

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Acknowledgements

Thanks are due to the referee for his valuable comments and useful suggestions and for his careful reading of the manuscript.

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Correspondence to M. Sghaier.

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Sghaier, M., Zaatra, M. The \(D_{w}\)-Laguerre–Hahn Forms of Class Zero. Mediterr. J. Math. 17, 185 (2020). https://doi.org/10.1007/s00009-020-01630-3

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Keywords

  • Orthogonal polynomials
  • Laguerre–Hahn forms
  • Difference operator

Mathematics Subject Classification

  • 33C45
  • 42C05