# On the product of the extreme zeros of Laguerre polynomials

Source: [On the product of the extreme zeros of Laguerre polynomials](<https://www.sota2.com/research/paper/68fa5c4a1e209131ce9cfa98>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:32:29.107Z

Authors: K. Castillo

Published: 2024-09-14T10:35:56.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2409.09405>)

[PDF](<https://arxiv.org/pdf/2409.09405.pdf>)