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

Revista Brasileira de Ensino de Física

关键词: Green’s function method;    Nonhomogeneous Helmholtz equation;    Homogeneous Dirichlet conditions.;   

DOI  :  10.1590/1806-9126-rbef-2021-0068

来源: DOAJ

【 摘 要 】

It is presented a way to obtain the closed form for Green’s function related to the nonhomogeneous one-dimensional 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 -α 2 ) is found in the process.

【 授权许可】

Unknown