Calculation of exponential integrals of real order

Abstract

In a previous paper a numerical method was presented for the generalized exponential integral function E _v (x), (x>0, v∊R), of interest for applications in astrophysics and nuclear physics in a general treatment context of this function. In the present work, we are mainly concerned with numerical features, above all as regards the relevant computational procedure and execution. Comparisons performed by means of a different algorithm ensure efficiency of the evaluation technique and the corresponding implementation, ERA, whose accuracy is confirmed by the results of the related error analysis.

Keywords:

• Generalized exponential-integral function
• real order
• numerical evaluation
• Taylor series expansion
• Tricomi's expansion