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Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one

  • Mabrouk Sghaier EMAIL logo , Mohamed Zaatra and Achraf Khlifi
Published/Copyright: September 11, 2018

Abstract

We give the system of Laguerre–Freud equations for the recurrence coefficients βn, γn+1, n0, of orthogonal polynomials with respect to a D-Laguerre–Hahn form (linear functional) of class one. The system is solved in the case when β0=-θ0, βn+1=θn-θn+1 and γn+1=-θn2 with θn0, n0. There are essentially three canonical cases.

MSC 2010: 33C45; 42C05

Acknowledgements

Grateful thanks go to Professor Francisco Marcellán for his careful reading, his constructive suggestions and his valuable comments on this paper which improved its presentation and readability. Special thanks go to the referee for his valuable comments and for his careful reading of the manuscript.

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Received: 2018-01-20
Revised: 2018-08-12
Accepted: 2018-08-15
Published Online: 2018-09-11
Published in Print: 2019-10-01

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