On the spacings between the successive zeros of the Laguerre polynomials

Stephane Chretien (1) , Sebastien Darses (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 I2M - Institut de Mathématiques de Marseille

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

Domaines: Mathématiques générales [math.GM]

Stephane Chretien, Sebastien Darses. On the spacings between the successive zeros of the Laguerre polynomials. Proceedings of the American Mathematical Society, 2015. ⟨hal-01270829⟩