An exact solution to the multi-dimensional line transfer equation

The theory of generalized analytic functions is used to obtain an exact closed form analytical solution to a transfer problem for spectral line radiation in a multi-dimensional atmosphere. The multi-dimensional full-space and half-space Green's functions so obtained are quite general and may be used, along with the corresponding orthogonality relationships, to obtain solutions to any general multi-dimensional radiative transfer problem involving model two-level atoms. An application of the method using perturbation techniques is illustrated.