On the spacings between the successive zeros of the Laguerre polynomials

Chrétien, Stéphane; Darses, Sébastien

doi:10.1090/proc/12574

On the spacings between the successive zeros of the Laguerre polynomials
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by Stéphane Chrétien and Sébastien Darses PDF

Proc. Amer. Math. Soc. 143 (2015), 4383-4388 Request permission

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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