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arXiv · 2409.09405

On the product of the extreme zeros of Laguerre polynomials

K. Castillo
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Abstract

The purpose of this note is twofold: firstly, it intends to bring to light an apparently unknown property of the product of the extreme zeros of Laguerre polynomials, which in a very particular case leads to a twenty-year-old conjecture for Hermite polynomials posed by Gazeau, Josse-Michaux, and Moncea while developing numerical methods in quantum mechanics; and secondly to progress towards the solution of this problem as an application of a parametric eigenvalue problem.

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K. Castillo. 2024-09-14. On the product of the extreme zeros of Laguerre polynomials. https://arxiv.org/abs/2409.09405

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