Logarithmic integral

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In mathematics, the logarithmic integral can refer to

{\rm li}(x) = {\rm PV} \int_0^x \frac{dt}{\ln t}
{\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.

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