Definition:Power Series/Real Domain

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

Let $\sequence {a_n}$ be a sequence in $\R$.

The series $\ds \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$, where $x \in \R$ is a variable, is called a power series in $x$ about the point $\xi$.