Logarithmic integral function
= Logarithmic integral function
{title2=$\operatorname{li}(x)$}
{wiki}
The <Cauchy principal value> integral $\operatorname{li}(x)=\operatorname{PV}\int_0^xdt/\log t$ is the logarithmic integral. The offset version $\operatorname{Li}(x)=\int_2^xdt/\log t$ differs by a constant and is often used with the <prime-counting function>. It has $\operatorname{Li}(x)\sim x/\log x$.