Helmholtz Green-function reciprocity ($G({\mathbf{r}}_1,{\mathbf{r}}_2)=G({\mathbf{r}}_2,{\mathbf{r}}_1)$)

Two Green functions of the same Helmholtz equation with the same homogeneous Robin boundary condition satisfy the displayed reciprocity by Green's second identity. It is a bilinear identity without complex conjugation, so it concerns the transpose rather than the Hermitian adjoint. In an exterior problem both kernels use the same radiation convention.