## Exponential Integrals | Extreme Optimization Numerical Libraries for .NET Professional |

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.

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 Ci(x). |

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