Derivation of the Green's function of the linear transport equation from the discrete-ordinate solution

Highlights: • The Green's function of transport equation with 2N discrete ordinates is calculated. • The solution can be written as a sum of exponential terms. • As N grows, the eigenvalue set tends to the spectrum obtained with the Case method. • By suitably summing the exponential terms, the rigorous solution is recovered. • The method presented here is very direct and requires only elementary calculus. - Abstract: A new, simple way to calculate the Green's function of the linear transport equation in a homogeneous, infinite medium is presented. The solution resorts to the corresponding Green's function for the discrete-ordinate method, which is readily obtainable, by using a suitable procedure to calculate the limit when the number of discrete directions tends to infinity