{"title":"On the product of the extreme zeros of Laguerre polynomials","authors":"K. Castillo","doi":"arxiv-2409.09405","DOIUrl":null,"url":null,"abstract":"The purpose of this note is twofold: firstly, it intends to bring to light an\napparently unknown property of the product of the extreme zeros of Laguerre\npolynomials, which in a very particular case leads to a twenty-year-old\nconjecture for Hermite polynomials posed by Gazeau, Josse-Michaux, and Moncea\nwhile developing numerical methods in quantum mechanics; and secondly to\nprogress towards the solution of this problem as an application of a parametric\neigenvalue problem.","PeriodicalId":501145,"journal":{"name":"arXiv - MATH - Classical Analysis and ODEs","volume":"10 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09405","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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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