I have a doubt about this, I think I am right about it, but I want to check since I couldn't find any similar question online. The problem is the following, very early introduction to Laurent Series. It goes like this.
$$\sum_{n=-\infty }^{\infty} \frac{(z+3i)^n}{2^n}$$
I want to make sure that, this series indeed does not represent any holomorphic function. Each subseries i.e.
$$\sum_{n=0 }^{\infty} \frac{(z+3i)^n}{2^n}$$ $$\sum_{n=1 }^{\infty} \frac{2^n}{(z+3i)^n}$$
has a radius of convergence: $|z+3i|<2$ for the first one and $|z+3i|>2$. So the set is empty in which this series converges, therefore, there is no holomorphic function defined by it. Thanks in advance.