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

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-...

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Bibliographic Details
Published in:	Proceedings of the American Mathematical Society Vol. 144; no. 12; pp. 5241 - 5249
Main Author:	Ben Romdhane, Neila
Format:	Journal Article
Language:	English
Published:	01-12-2016
Subjects:	Zeros component sets Laguerre and $q$-Laguerre polynomials Brenke type polynomials d$-orthogonal Laguerre and $q$-Laguerre polynomials
Online Access:	Get full text
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Summary:	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.
ISSN:	0002-9939 1088-6826
DOI:	10.1090/proc/13164