Definition:Power Series

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

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

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