An algorithm for exponential integrals of real order

Abstract

The solution of many problems in radiative transfer and transport theory, requires calculations of real-order exponential integrals,E s (x). We consider a composite algorithm based on a recursive evaluation ofE s (x), $$s \in \mathbb{R}$$ ,x>0, starting from a suitable initial value in the region of positives andx arguments, which ensures the numerical stability of the involved recurrences.