On the zeros of $d$-orthogonal Laguerre polynomials and their $q$-analogues
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Abstract:
In this paper, we give some properties of the zeros of special families of Brenke type polynomials. In particular, we consider an extension of Laguerre polynomials known as $d$-orthogonal Laguerre polynomials. For these polynomials, we prove that all the zeros are simple, positive and interlaced. A $q$-analogue is considered as well.References
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Additional Information
- Neila Ben Romdhane
- Affiliation: École Supérieure des Sciences et de Technologie de Hammam Sousse, University of Sousse, Tunisia
- MR Author ID: 823687
- Email: neila.benromdhane@ipeim.rnu.tn
- Received by editor(s): July 11, 2015
- Received by editor(s) in revised form: February 14, 2016
- Published electronically: June 3, 2016
- Communicated by: Walter Van Assche
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 5241-5249
- MSC (2010): Primary 42C05, 33C45, 33D45
- DOI: https://doi.org/10.1090/proc/13164
- MathSciNet review: 3556268