Definition:Power Series/Complex Domain

Definition
Let $\xi \in \C$ be a complex number.

Let $\left \langle {a_n} \right \rangle$ be a sequence in $\C$.

The series $\displaystyle \sum_{n \mathop = 0}^\infty a_n \left({z - \xi}\right)^n$, where $z \in \C$ is a variable, is called a power series in $z$ about the point $\xi$.