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{{Short description|Special function defined by an integral}}
{{Redirect|Li(x)|the polylogarithm denoted by Li<sub>''s''</sub>(''z'')|Polylogarithm}}
[[File:Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg|alt=Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D|thumb|Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D]]▼
{{Use American English|date = January 2019}}
▲[[File:Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D.svg|alt=Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D|thumb|Plot of the logarithmic integral function li(z) in the complex plane from -2-2i to 2+2i with colors created with Mathematica 13.1 function ComplexPlot3D]]
In [[mathematics]], the '''logarithmic integral function''' or '''integral logarithm''' li(''x'') is a [[special function]]. It is relevant in problems of [[physics]] and has [[number theory|number theoretic]] significance. In particular, according to the [[Prime number theorem]] it is a very good [[approximation]] to the [[prime-counting function]], which is defined as the number of [[prime numbers]] less than or equal to a given value <math>x</math>. [[Image:Logarithmic integral function.svg|thumb|right|300px|Logarithmic integral function plot]]
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