Dilogarithm
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The dilogarithm is the function $$L_2(z)=\displaystyle\sum_{k=1}^{\infty} \dfrac{z^k}{k^2},$$ which is a special case of the polylogarithm.
Properties
Theorem: The following formula holds: $$L_2(z)=-L_2 \left( \dfrac{1}{z} \right) - \dfrac{1}{2} \left( \log(z) \right)^2 + \pi i \log(z) + \dfrac{\pi^2}{3}.$$
Proof: █
