一维亥姆霍兹方程的格林函数:傅里叶正弦级数的封闭解

Q4 Social Sciences

Revista Brasileira De Ensino De Fisica Pub Date : 2021-01-01 DOI:10.1590/1806-9126-RBEF-2021-0068

A. Castro

{"title":"一维亥姆霍兹方程的格林函数:傅里叶正弦级数的封闭解","authors":"A. Castro","doi":"10.1590/1806-9126-RBEF-2021-0068","DOIUrl":null,"url":null,"abstract":"It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous onedimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑∞ k=1 sin kx sin ky/(k 2 − α2) is found in the process.","PeriodicalId":49620,"journal":{"name":"Revista Brasileira De Ensino De Fisica","volume":"51 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series\",\"authors\":\"A. Castro\",\"doi\":\"10.1590/1806-9126-RBEF-2021-0068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous onedimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑∞ k=1 sin kx sin ky/(k 2 − α2) is found in the process.\",\"PeriodicalId\":49620,\"journal\":{\"name\":\"Revista Brasileira De Ensino De Fisica\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Brasileira De Ensino De Fisica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1590/1806-9126-RBEF-2021-0068\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Social Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Revista Brasileira De Ensino De Fisica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1590/1806-9126-RBEF-2021-0068","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Social Sciences","Score":null,"Total":0}

引用次数: 0

摘要

给出了一种由傅里叶正弦级数表示得到具有齐次狄利克雷条件的非齐次一维亥姆霍兹方程格林函数的封闭形式的方法。在此过程中找到了级数∑∞k=1 sin kx sin ky/(k 2−α2)的和的封闭形式。

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

Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series

It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous onedimensional Helmholtz equation with homogeneous Dirichlet conditions on the boundary of the domain from its Fourier sine series representation. A closed form for the sum of the series ∑∞ k=1 sin kx sin ky/(k 2 − α2) is found in the process.

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

Revista Brasileira De Ensino De Fisica 物理-物理：综合

CiteScore

0.50

自引率

0.00%

发文量

102

审稿时长

6-12 weeks

期刊介绍： The Revista Brasileira de Ensino de Física - RBEF - is an open-access journal of the Brazilian Physical Society (SBF) devoted to the improvement of Physics teaching at all academic levels. Through the publication of peer-reviewed, high-quality papers, we aim at promoting Physics and correlated sciences, thus contributing to the scientific education of society. The RBEF accepts papers on theoretical and experimental aspects of Physics, materials and methodology, history and philosophy of sciences, education policies and themes relevant to the physics-teaching and research community.