## Franklin's Notes

### Complex Taylor series

Given a basepoint $z_0$ and a function $f$ that is holomorphic in some region $\Omega$, it is always possible to express $f$ in the form where $f_{n+1}$ is also a holomorphic function in $\Omega$. We can think of $f_{n+1}$ as a "quotient" of $f$ by $(z-z_0)^{n+1}$, and the first $n+1$ terms as comprising a "remainder" of $f$ divided by $(z-z_0)^{n+1}$.