On the spacings between the successive zeros of the Laguerre polynomials

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

arXiv commentThis version proposes an improved bound and more comparisons with previous works