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:
$$\Ei(x) = -\int_{-x}^{\inf}\frac{e^{-t}\,dt}{t}$$The E1 function is related to the exponential integral by the relation
$$E_1(x) = -\Ei(-x)$$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.
Method | Description |
|---|---|
The exponential integral Ei(x). | |
The exponential integral E1(x). | |
The logarithmic integral li(x). | |
The cosine integral Ci(x). | |
The sine integral Si(x). |