Astronomy and Astrophysics – Astrophysics
Scientific paper
May 1972
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972ap%26ss..16..241b&link_type=abstract
Astrophysics and Space Science, Volume 16, Issue 2, pp.241-248
Astronomy and Astrophysics
Astrophysics
4
Scientific paper
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.
Bellman Richard
Ueno Sueo
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