Derives nonlinear integral equations for a generalized redistribution function M(mu, U, omega_0) that adds thermal emission to the classical isotropic scattering problem and reduces to H(mu) when emission vanishes.
Numerical evaluation of Chandrasekhar's H-function, its first and second differential coefficients, its pole and moments from the new form for plane parallel scattering atmosphere in radiative transfer
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abstract
In this paper, the new forms obtained for Chandrasekhar's H- function in Radiative Transfer by one of the authors both for non-conservative and conservative cases for isotropic scattering in a semi-infinite plane parallel atmosphere are used to obtain exclusively new forms for the first and second derivatives of H-function . The numerics for evaluation of zero of dispersion function, for evaluation of H-function and its derivatives and its zeroth, the first and second moments are outlined. Those are used to get ready and accurate extensive tables of H-function and its derivatives, pole and moments for different albedo for scattering by iteration and Simpson's one third rule . The schemes for interpolation of H-function for any arbitrary value of the direction parameter for a given albedo are also outlined. Good agreement has been observed in checks with the available results within one unit of ninth decimal
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Effect of Thermal Emission in Isotropic Scattering Atmospheres: An Invariant-Embedding Extension of Chandrasekhar's $H(\mu)$-Function
Derives nonlinear integral equations for a generalized redistribution function M(mu, U, omega_0) that adds thermal emission to the classical isotropic scattering problem and reduces to H(mu) when emission vanishes.