On convergence,asymptotic behaviour and computational algorithm of generalized exponential integral functions arising in a radiative transfer

In this paper, we investigate uniform convergence of the generalized exponential integral functions (GEI) arising in the study of radiative transfer in a two-dimensional planar-medium and anisotropic scattering in a multidimensional medium. Using the uniform convergence, we study the properties and asymptotic behaviour of the GEI functions. We also give an efficient algorithm for the computations of the values of the GEI functions.