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On the spacings between the successive zeros of the Laguerre polynomials


Authors: Stéphane Chrétien and Sébastien Darses
Journal: Proc. Amer. Math. Soc. 143 (2015), 4383-4388
MSC (2010): Primary 33C45; Secondary 26C10
Published electronically: April 21, 2015
MathSciNet review: 3373936
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Abstract: We propose a simple uniform lower bound on the spacings between the successive zeros of the Laguerre polynomials $ L_n^{(\alpha )}$ for all $ \alpha >-1$. Our bound is sharp regarding the order of dependency on $ n$ and $ \alpha $ in various ranges. In particular, we recover the orders given in a work of Ahmed, Laforgia and Muldoon (1982) for $ \alpha \in (-1,1]$.


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Stéphane Chrétien
Affiliation: Laboratoire de Mathématiques, UMR 6623, Université de Franche-Comté, 16 route de Gray, 25030 Besancon, France
Email: stephane.chretien@univ-fcomte.fr

Sébastien Darses
Affiliation: I2M, UMR 6632, Aix-Marseille Université, Technopôle Château-Gombert, 39 rue Joliot Curie, 13453 Marseille Cedex 13, France — and — Université de Franche-Comté, 16 route de Gray, 25030 Besancon, France
Email: sebastien.darses@univ-amu.fr

DOI: https://doi.org/10.1090/proc/12574
Received by editor(s): March 10, 2014
Received by editor(s) in revised form: June 20, 2014
Published electronically: April 21, 2015
Communicated by: Sergei K. Suslov
Article copyright: © Copyright 2015 American Mathematical Society