Exponential Integrals

Exponential integrals arise in many engineering applications. At least three different definitions have been used in the literature. Here, we use the most common definition:

The E1 function is related to the exponential integral by the relation

E1(x) = Ei(x).

The logarithmic integral is related to the exponential integral by the relation

li(x) = Ei(ln x).

The sine and cosine integrals are related to the exponential integral by the relation

Ei(ix) = Ci(x) + iSi(x).

The Special class provides static methods for evaluating the exponential integral and related functions for real arguments, as listed in the table below.