Extended Laguerre inequalities and a criterion for real zeros

2009/11/05 by David A. Cardon, Cardon, David A. · 1 citation
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.CV

paper · pdf · doi:10.48550/arxiv.0911.1122

The paper is based on a talk given at the 7th ISAAC Congress held at Imperial College in London in July 2009

arxiv created 2009/11/05 · openalex publication_date 2009/11/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f(z)=e^-bz2f₁(z) where b ≥ 0 and f₁(z) is a real entire function of genus 0 or 1. We give a necessary and sufficient condition in terms of a sequence of inequalities for all of the zeros of f(z) to be real. These inequalities are an extension of the classical Laguerre inequalities.

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