Definition:Power Series

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 $x$ is a variable, is called a power series in $x$ about the point $\xi$.

Sources

• K.G. Binmore: Mathematical Analysis: A Straightforward Approach (1977)... (previous)... (next): $\S 15.1$