Mathematics
Scientific paper
Aug 1980
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980ap%26ss..71...25d&link_type=abstract
Astrophysics and Space Science, vol. 71, no. 1, Aug. 1980, p. 25-35.
Mathematics
4
Atmospheric Models, Laplace Transformation, Linear Equations, Radiative Transfer, Singular Integral Equations, Boundary Value Problems, Differential Equations, Distribution (Property), Operators (Mathematics), Surface Properties
Scientific paper
The paper considers the astrophysical problem of a finite atmosphere having an intensity distribution at both surfaces with definite forms of the scattering function and the source function. The basic integrodifferential equation for the intensity distribution at any optical depth is subjected to the finite Laplace transform, and linear integral equations for the surface quantities are obtained. These equations are then transformed into linear singular equations by the use of Plemelj's formulas. The singular equations are solved in terms of Chandrasekhar's X-Y equations.
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