Radiative transfer in plane-parallel media and Cauchy integral equations II. The H-function

In the central part of this paper, we revisit the classical study of the H-function defined as the unique solution, regular in the right complex half-plane, of a Cauchy integral equation. We take advantage of our work on the N-function published in the first article of this series. The H-function is then used to solve a class of Cauchy integral equations occurring in transfer problems posed in plane-parallel media. We obtain a concise expression of the unique solution analytic in the right complex half-plane, then modified with the help of the residue theorem for numerical calculations.