Definition of polylog for all complex $\text{z}$

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What are the different definitions of:

$$\text{Li}_\text{n}\left(\text{z}\right)$$

For all possible $\text{z}$???

I know that when $\left|\text{z}\right|<1$ it is defined by:

$$\text{Li}_\text{n}\left(\text{z}\right)=\sum_{\text{k}=1}^\infty\frac{\text{z}^\text{k}}{\text{k}^\text{n}}$$