Green’s function for the one-dimensional Helmholtz equation: closed-form solution from its Fourier sine series - Castro, Antonio S. De [UNESP] (Sociedade Brasileira de Física, 2021)
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⁡k⁢x⁢sin⁡k⁢y/(k2-α2) is found in the process.
Keywords: Green’s function method; Nonhomogeneous Helmholtz equation; Homogeneous Dirichlet conditions.