Yes, some of them are geometric series, and some of $e^{z}$, $\sin(z)$, $\sinh(z)$ and so on. However some can be derived from those, ether by substitution (f.e. $z^2$ instead of $z$), some by integration, differentiation, multiplication by $z^m$ or combination of both. F.e. consider geometric $\dfrac{1}{1-z}$. Integratinfg we can get power series for $-\Log (1-z)$, diffeerentiating for $\frac{1}{(1-z)^m}$ ,...