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arXiv · 1402.6603

On the spacings between the successive zeros of the Laguerre polynomials

Stephane Chretien·Sebastien Darses
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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 \cite{ahmed} for $\alpha \in (-1,1]$.

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Stephane Chretien, Sebastien Darses. 2014-02-19. On the spacings between the successive zeros of the Laguerre polynomials. https://arxiv.org/abs/1402.6603

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