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- On the spacings between the successive zeros of the Laguerre polynomials arxiv link

Auteur(s): Chretien Stephane, Darses S.

(Article) Publié: Proceedings Of The American Mathematical Society, vol. p. (2015)


Ref HAL: hal-01270829_v1
Ref Arxiv: 1402.6603
Ref. & Cit.: NASA ADS
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Résumé:

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 $\alpha \in (-1,1]$.



Commentaires: This version proposes an improved bound and more comparisons with previous works