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Series for reciprocal of polylogarithm?
The series representation of a polylogarithm of order $s$ is given by
$$\text{Li}_s(z) = \sum_{k=1}^{\infty}\frac{z^k}{k^s}$$
Are there any simplified expressions for $\dfrac{1}{\text{Li}_s(z)}$? ...
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Proving $\text{Li}_3\left(-\frac{1}{3}\right)-2 \text{Li}_3\left(\frac{1}{3}\right)= -\frac{\log^33}{6}+\frac{\pi^2}{6}\log 3-\frac{13\zeta(3)}{6}$?
Ramanujan gave the following identities for the Dilogarithm function:
$$
\begin{align*}
\operatorname{Li}_2\left(\frac{1}{3}\right)-\frac{1}{6}\operatorname{Li}_2\left(\frac{1}{9}\right) &=\frac{{...
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