Category:Definitions/Examples of Power Series

This category contains definitions of examples of Power Series.

Real Domain

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 (real) power series in $x$ about the point $\xi$.

Complex Domain

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

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

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