# Compute $\operatorname{Li}_{3}\left(\frac{1}{2} \right)$

Where could I find a proof of the identity

$$\operatorname{Li}_{3}\left(\frac{1}{2} \right) = \sum_{n=1}^{\infty}\frac{1}{2^n n^3}= \frac{1}{24} \left( 21\zeta(3)+4\ln^3 (2)-2\pi^2 \ln2\right)$$

?

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Maybe here? books.google.fr/… –  julien Feb 3 at 16:44