Definition:Power Series/Real Domain

Definition
Let $\xi \in \R$ be a real number.

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

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