Astrophysics and Space Science

, Volume 16, Issue 2, pp 241–248 | Cite as

Invariant imbedding and Chandrasekhar's planetary problem of radiative transfer

  • Richard Bellman
  • Sueo Ueno


In connection with Chandrasekhar's planetary problem of radiative transfer the total scattering and the diffuse transmission functions have been discussed by several authors (cf. Chandrasekhar, 1950; van de Hulst, 1948; Sobolev, 1948; Bellman,et al., 1967; Kagiwada and Kalaba, 1971). With the aid of the Bellman-Krein formula for the resolvent kernel of the auxiliary equation governing the source function, we show how the invariant imbedding equations governing the diffuse scattering and transmission functions can readily be obtained. So far as we know, the Cauchy system of the functional equations for the scattering and transmission functions is new and is well-suited for the numerical computation.


Numerical Computation Functional Equation Radiative Transfer Source Function Transmission Function 
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Copyright information

© D. Reidel Publishing Company 1972

Authors and Affiliations

  • Richard Bellman
    • 1
  • Sueo Ueno
    • 2
  1. 1.Departments of Mathematics, Electrical Engineering, and MedicineUniv. of Southern CaliforniaLos AngelesUSA
  2. 2.Department of AstronomyUniversity of Southern CaliforniaLos AngelesUSA

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