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On the zeros of $ d$-orthogonal Laguerre polynomials and their $ q$-analogues


Author: Neila Ben Romdhane
Journal: Proc. Amer. Math. Soc. 144 (2016), 5241-5249
MSC (2010): Primary 42C05, 33C45, 33D45
DOI: https://doi.org/10.1090/proc/13164
Published electronically: June 3, 2016
MathSciNet review: 3556268
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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.


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Additional Information

Neila Ben Romdhane
Affiliation: École Supérieure des Sciences et de Technologie de Hammam Sousse, University of Sousse, Tunisia
Email: neila.benromdhane@ipeim.rnu.tn

DOI: https://doi.org/10.1090/proc/13164
Keywords: Zeros, Laguerre and $q$-Laguerre polynomials, Brenke type polynomials, component sets, $d$-orthogonal Laguerre and $q$-Laguerre polynomials
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
Article copyright: © Copyright 2016 American Mathematical Society

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