![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Plot_of_the_exponential_integral_function_E_n%2528z%2529_with_n%253D2_in_the_complex_plane_from_-2-2i_to_2%252B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg/640px-thumbnail.svg.png&w=640&q=50)
Exponential integral
Special function defined by an integral / From Wikipedia, the free encyclopedia
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In mathematics, the exponential integral Ei is a special function on the complex plane.
Not to be confused with other integrals of exponential functions.
![Plot of the exponential integral function E n(z) with n=2 in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D](http://upload.wikimedia.org/wikipedia/commons/thumb/c/ce/Plot_of_the_exponential_integral_function_E_n%28z%29_with_n%3D2_in_the_complex_plane_from_-2-2i_to_2%2B2i_with_colors_created_with_Mathematica_13.1_function_ComplexPlot3D.svg/640px-thumbnail.svg.png)
It is defined as one particular definite integral of the ratio between an exponential function and its argument.