Chandrasekhar's H-function revisited. (May 2020) - Nagirner, Dmitrij I.; Ivanov, Vsevolod V.
Highlights: New unusual properties of Chandrasekhar's H -function are established. Abstract: The Chandrasekhar H -function plays an important role in a wide class of problems of analytical radiative transfer theory. The H -function is the solution of well-known integral equations, both non-linear and linear. The physics of a particular problem under consideration determines the form of the so-called characteristic and dispersion functions, Ψ( μ ) and T ( μ ), respectively. They appear in H -equations and determine their solutions. We show that Ψ( μ ) and T ( μ ) can be restructured in such a way that the solutions of H -equations transforms from H ( μ ) to H n ( μ ), n = 2, 3, 4, … provided Ψ( μ ) and T ( μ ) are replaced with Ψ n ( μ ) and Tn ( μ ). The structure of the non-linear and linear H -equations does not change under this transformation. The basis of this restructuring is a recursion relation that gives Ψ n ( μ ) and Tn ( μ ) in terms of Ψ( μ ) and T ( μ ).