Logarithmic integral

The logarithmic integral is $$\mathrm{li}(x) = \displaystyle\int_0^x \dfrac{1}{\log(t)} \mathrm{d}t,$$ where $\log$ denotes the logarithm.

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  Graph of $\mathrm{li}$.

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  Domain coloring of $\mathrm{li}$.

Properties

Relationship between logarithmic integral and exponential integral
Prime number theorem, logarithmic integral

See Also

Prime counting function

$\ast$-integral functions

Cosine integral

Cosh integral

Exp integral $E_n$

Exp integral $\mathrm{Ei}$

Fresnel $C$

Fresnel $S$

Gudermannian

Inverse $\mathrm{gd}$

Sine integral

Log integral

Sinh integral