Evaluation of generalized exponential integral function using binomial expansion theorems

Using binomial expansion theorems, a new approach for numerical analyzing of the generalized exponential integral (GEIs) functions are presented in this paper. Established formulas are utilized in the computation of GEIs functions, with arising in the analysis of radiative transfer in a two-dimensional planar medium. Evaluation of GEIs functions for different values of the parameters, show the efficiencies of the new approach. The numerical results illustrate clearly a further reduction in calculation times. Several numerical examples, which illustrate the effectiveness of the method, are presented and the results are compared, with those reported in the literature.