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

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 − α 2 ) is found in the process.