# Logarithmic integral

From specialfunctionswiki

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

Domain coloring of $\mathrm{li}$.

# Properties

Relationship between logarithmic integral and exponential integral

Prime number theorem, logarithmic integral

# See Also

# References

- James Whitbread Lee Glaisher:
*On certain definite integrals involving the exponential-integral*(1881)... (previous)... (next) - 1964: Milton Abramowitz and Irene A. Stegun:
*Handbook of mathematical functions*... (previous) ... (next): $5.1.3$

**Logarithm and friends**

**$\ast$-integral functions**