Does anybody know where I could find the expression for $$\frac{\partial}{\partial s}\mathrm{Li}_s(z)\bigg|_{s=0}$$ or something similar?
2026-04-29 21:10:16.1777497016
Polylogarithm - derivative with respect to order
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For every $|z|<1$, we have $$ \frac{\partial}{\partial s}\mathrm{Li}_s(z)\Big|_{s=0} = -\sum_{n=1}^\infty \log (n)\frac{z^n}{n^s} \Big|_{s=0} = -\sum_{n=1}^\infty \log(n)\,z^n $$
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