{"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}
引用次数: 0
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.
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.
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