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on the (double) discontinuity of dilogarithm along a branch cut
Define the function
$$Li_s(z)=\sum_{k=1}^\infty \frac{z^k}{k^s}$$
for |z|<1. Let's focus on $s=2$.
It can be extended to a holomorphic function on $\mathbb C \setminus [1,\infty)$
$$Li_2(z)= -\...
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