Linear integral equations for Chandrasekhar's S and T functions are derived from the solution for the half-space albedo problem by using the principles of invariance. This procedure is a generalization of the method by which the thick-slab asymptotic solutions for the S and T functions are obtained by combining the solutions for the half-space ordinary Milne and albedo problems. Approximate solutions can be calculated by iteration. Explicit expressions for the zero'th-order approximations are given in terms of Ambarzumian-Chandrasekhar's H function, and Busbridge's q polynomials. Case's full-range normal mode expansion is then applied to find the approximate solutions for the albedo problem. The method by which the approximate solutions for the Green's function problem can be obtained is also indicated.