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arXiv · 0911.1122

Extended Laguerre inequalities and a criterion for real zeros

David A. Cardon
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Abstract

Let $f(z)=e^{-bz^2}f_1(z)$ where $b \geq 0$ and $f_1(z)$ 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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David A. Cardon. 2009-11-05. Extended Laguerre inequalities and a criterion for real zeros. https://arxiv.org/abs/0911.1122

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