Abstract
In recent years approximate solutions for line-transfer problems using a kernel representation have been discussed by several authors (cf. Avrett and Loeser, 1966; Hummer and Rybicki, 1967). In this paper, extending an invariant imbedding method to the line-transfer problem with a kernel approximation as a sum of exponentials, we show how to get an exact solution of Milne's integral equation for the frequency-independent line source function with the aid of the resolvent kernel. A Cauchy system for an auxiliary function and the resolvent is suitable for numerical computation by means of high-speed digital computers.
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