On the spacings between the successive zeros of the Laguerre polynomials

2014/02/19 by Stéphane Chrétien, Chretien, Stephane, Darses, Sebastien
Mathematics · #Advanced Combinatorial Mathematics #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials

paper · doi:10.48550/arxiv.1402.6603

openalex publication_date 2014/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a simple uniform lower bound on the spacings between the successive zeros of the Laguerre polynomials L_n^(α) for all α>-1. Our bound is sharp regarding the order of dependency on n and α in various ranges. In particular, we recover the orders given in \citeahmed for α∈ (-1,1].

Related

• Zeros of quasi-orthogonal q-Laguerre polynomials
• A Short Note On Laguerre Polynomials
• On zeros of polynomials and allied functions satisfying second order differential equations
• Analysis of Laguerre's method applied to find the roots of unity
• Interlacing Families III: Sharper Restricted Invertibility Estimates