Category:Definitions/Power Series

From ProofWiki
Jump to: navigation, search

This category contains definitions related to Power Series.
Related results can be found in Category:Power Series.


Real Domain

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

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


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


Complex Domain

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

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


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