Logarithmic integral

In mathematics, the logarithmic integral can refer to

• The logarithmic integral function, defined as

${\rm {li}}(x)={\rm {PV}}\int _{0}^{x}{\frac {dt}{\ln t}}$

• The offset logarithmic integral, defined as

${\rm {Li}}(x)={\rm {li}}(x)-{\rm {li}}(2)=\int _{2}^{x}{\frac {dt}{\ln t}}$

• The logarithmic integral defined as

$\int _{-\infty }^{\infty }{\frac {M(t)}{1+t^{2}}}dt$

and discussed in Paul Koosis, The Logarithmic Integral, volumes I and II, Cambridge University Press, second edition, 1998.