The analytical representation of eigenfunctions for finite moments method approximations of radiative transport equations is constructed in slab geometry problems. The truncated balance algorithm is used. An angle dependence of discrete eigenfunctions is determined by discrete characteristic equation solutions. It is established that space-dependent factors of discrete eigenfunctions are Pade approximations of the exponential functions and correspond to the original transport problem eigenfunctions. This technique proves to be useful for analyzing solvability and accuracy of finite moment approximations and also for developing computational algorithms. Slowly changing eigenfunctions are included in the regular component of the optically thick slab problem solution. Coarse-mesh algorithms or diffusion approximations at specific boundary conditions can be used to determine these components. Other eigenfunctions determine the singular component of the mesh solution. This component represents the transition regime on coarse meshes with typical oscillations or with a slow decrease in boundary layers. It is strongly different from the singular component of the exact solution.