Miscellaneous Functions
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Exponential Integral and Related Functions

The exponential integral is defined as

Some books define the exponential integral of order 1 as the exponential integral:

It has the following properties and special results:

where gamma is Euler's constant.

Sine and Cosine Integrals

The sine and cosine integrals are defined as:

Sine Integral Cosine Integral

They have the following properties and special results:

Ei(0)=-Inf
Ci(-x)=Ci(x)+Pi*i

where gamma is Euler's constant.

Fresnel Integrals

The Fresnel sine and cosine integrals are defined as:

Fresnel Sine Integral Fresnel Cosine Integral

They have the following properties and special results:

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