An extension of the resolvent procedure as applied to the solution of the photon diffusion equation in a finite homogeneous slab. The technique is extended to determine the integro-differential equations for the photon emergence probability in a finite isotropically scattering flat layer of arbitrary stratification. Several integro-differential equations for Chandrasekhar's X and Y functions are found, taking into consideration the polarity of the radiation. 22 pp. Bibliog.