Integral equations satisfied by the H- X- and Y-functions and the albedo problem |
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Institution: | Transfer Group, Centre de Recherche Astronomique de Lyon (UMR 5574 du CNRS), Observatoire de Lyon, 9 avenue Charles André, 69561 Saint-Genis-Laval Cedex, France |
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Abstract: | We come back to a nonlinear integral equation satisfied by the function H, which is distinct from the classical H-equation. Established for the first time by Busbridge (1955), it appeared occasionally in the literature since then. First of all, this equation is generalized over the whole complex plane using the method of residues. Then its counterpart in a finite slab is derived; it consists in two series of integral equations for the X- and Y-functions. These integral equations are finally applied to the solution of the albedo problem in a slab. |
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Keywords: | Transport (or transfer) theory Plane-parallel geometry Isotropic scattering Integral equations Functions H X and Y Albedo problem |
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