On a tricomi series representation for the generalized exponential integral

Abstract

We consider an expression of the generalized exponential integral E _v (x), in terms of the modified incomplete gamma function γ ^∗(a,x). By means of a Tricomi series representation for γ ^∗(a,x), a proper expansion of E _v (x) is obtained, which may represent a useful tool in applications. Numerical results are also presented and discussed.

Keywords:

• Generalized exponential integral functions
• numerical evaluation
• Tricomi's expansion