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Can this formula for $\zeta(3)$ be proven or simplified further?
This question is related to the equivalence of formulas (1) and (2) below where formula (1) is from a post on the Harmonic Series Facebook group and formula (2) is based on evaluation of the integral ...
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How can we show that the multi-polylogarithmic function $L_{\underbrace{1,\ldots,1}_n}(z)=\frac{1}{n!}(L_1(z))^n$
How can we show that the multi-polylogarithmic function
$$L_{\underbrace{1,\ldots,1}_n}(z)=\frac{1}{n!}(L_1(z))^n.$$
Here $L_1(z)=-log(1-z)$.
I know that $\frac{d}{dz}L_{k_1,\ldots,k_r}(z)=\frac{1}{1-...
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