\begin{definition}[Definition:Exponential Function/Complex/Power Series Expansion]
Let $\exp: \C \to \C \setminus \set 0$ denote the '''(complex) exponential function'''.
The '''exponential function''' can be defined as a (complex) power series:
{{begin-eqn}}
{{eqn | l = \exp z
      | r = \sum_{n \mathop = 0}^\infty \frac {z^n} {n!}
      | c = 
}}
{{eqn | r = 1 + \frac z {1!} + \frac {z^2} {2!} + \frac {z^3} {3!} + \cdots + \frac {z^n} {n!} + \cdots
      | c = 
}}
{{end-eqn}}
The complex number $\exp z$ is called the '''exponential of $z$'''.
\end{definition}