An alternate form of Ueno's X- and Y-equations for inhomogeneous atmospheres

Abstract

Starting from the global form of the equations of transfer, the nonlinear integral equations in the X-, Y-, X^∗ -, and Y^∗-functions for inhomogeneous atmospheres, similar to the Chandrasekhar equations for homogeneous atmospheres, are derived. Their relations to Ueno's and Chandrasekhar's equations are discussed and two approaches to the treatment of the problem of uniqueness of the solutions of these equations are suggested.