Exact solution of the problem of diffuse reflection and transmission in Rayleigh scattering by use of the Laplace transform and the theory of linear singular operators

DOI10.1007/BF00648254zbMath0393.45005MaRDI QIDQ1252491

Rabindra Nath Das

Publication date: 1979

Published in: Astrophysics and Space Science (Search for Journal in Brave)

zbMATH Keywords

Laplace TransformDiffuse Reflection And TransmissionLinear Singular OperatorsRayleigh Scattering

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Laplace transform (44A10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Radiative transfer in astronomy and astrophysics (85A25)

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Solution of Riemann-Hilbert problems for determination of new decoupled expressions of Chandrasekhar's \(X\)- and \(Y\)-functions for slab geometry in radiative transfer

Cites Work

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• Elementary solutions of the transport equation and their applications
• Exact solution of the equation for the problem of diffuse reflection and transmission with a scattering function \(\omega_0(1+x\cos \Theta)\) by the method of Laplace transform and theory of linear singular integral equation
• Exact solution of the problem of diffuse reflection and transmission by the method of Laplace transform and linear singular operators
• The Complete Rayleigh-Scattered Field Within a Homogeneous Plane-Parallel Atmosphere

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