I'm asked to discuss the analytic continuation of the function
$$\sum_{n=0}^{\infty} \frac{z^{n+1}}{n+1}$$ for |z|<1
The following hint is also provided
$$\sum_{n=0}^{\infty} \frac{z^{n+1}}{n+1} = \int_{0}^{z}\sum_{n=0}^{\infty} z^{*n}dz^*$$
I'm unsure how to interpret the problem. What can be said about its analytic continuation? Is the integral providing a clue as to where it can be continued?