On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE_n which is denoted as _n(). The main result of this analysis enables us to establish a two-term recurrence formula for _n(0) and a three-term recurrence formula for _n(); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.