Integrals involving an exponential integral function and exponentials arising in the solution of radiation transfer

The solution of the equation of radiative transfer for a participating medium generally results in the evaluation of integrals involving a product of an exponential integral function or an exponential with a polynomial. Although expressions are available in the literature for the evaluation of such integrals, which appear to be structurally easy and simple to program, they are found to be not so accurate for certain parameters involved. To overcome such difficulties, alternative, computationally more accurate, analytic expressions are presented, and numerical techniques for their evaluation are discussed.