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

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

2006-01-16

arxiv.org/abs/astro-ph/0601349v1

Astronomy and Astrophysics

Astrophysics

19 pages, Transport Theory and Statistical Processes, submitted January 2003

Scientific paper

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.

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