RADIATIVE TRANSFER IN PLANE-PARALLEL MEDIA AND CAUCHY INTEGRAL EQUATIONS. I. THEN-FUNCTION
- 11 January 2002
- journal article
- research article
- Published by Taylor & Francis in Transport Theory and Statistical Physics
- Vol. 31 (7) , 659-671
- https://doi.org/10.1081/tt-120015629
Abstract
We return to the Cauchy integral equations encountered in transfer problems when formulated in plane-parallel media. Light scattering is assumed isotropic for simplicity. The analytical properties of the classical N-function are reviewed. This function is sectionally analytic in the complex plane cut along the segment [0, 1]. Its domain is extended to the whole complex plane, except at +1 where it diverges. We write down the functional relations satisfied by N outside [0, 1] and extend them on the cut with the help of Plemelj's formulae. This article is an introduction to a revisited derivation of the functions H and X, Y of plane-parallel media from the singular integral equations they satisfy.Keywords
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