On the spacings between the successive zeros of the Laguerre polynomials

Stephane Chretien, Sebastien Darses

Published 2014-02-19, updated 2014-06-22Version 3

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 \cite{ahmed} for $\alpha \in (-1,1]$.