论拉盖尔多项式极值的乘积

arXiv - MATH - Classical Analysis and ODEs Pub Date : 2024-09-14 DOI:arxiv-2409.09405

K. Castillo

{"title":"论拉盖尔多项式极值的乘积","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":"{\"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}","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

摘要

本说明有两个目的：首先，它旨在揭示拉盖尔多项式极值乘积的一个显然未知的性质，在一个非常特殊的情况下，该性质导致了 Gazeau、Josse-Michaux 和 Monceaw 在开发量子力学数值方法时提出的赫尔米特多项式的一个长达 20 年的猜想；其次，作为参数特征值问题的应用，它在解决该问题方面取得了进展。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the product of the extreme zeros of Laguerre polynomials

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Classical Analysis and ODEs

自引率

0.00%

发文量