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Using Contour Integral to find the value of $\int_{-1}^{+1}\frac{\ln{(1+t)}}{t}dt$
$\newcommand{LogI}{\operatorname{Li}}$
We know that the value of $\LogI_{2}(-1)$ is -$\frac{\pi^2}{12}$ and $\LogI_{2}(1)$ is $\frac{\pi^2}{6}$. The value of the polylogarithms has already been ...
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Contour Integral involving Dilogarithmic functions
I am considering the contour integral:
$\int Li_2\left( \frac{1-z}{2}\right)Li_2\left( \frac{z-1}{2z}\right) \frac{dz}{z}$.
The contour of integration is the unit circle excluding the pole $z = 0$. $...
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