Category:Definitions/Power Series
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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 $\ds \sum_{n \mathop = 0}^\infty a_n \paren {x - \xi}^n$, where $x \in \R$ is a variable, is called a power series in $x$ about the point $\xi$.
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 $\xi$.
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Definitions/Power Series"
The following 23 pages are in this category, out of 23 total.
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- Definition:Radius of Convergence
- Definition:Radius of Convergence of Complex Power Series
- Definition:Radius of Convergence of Real Power Series
- Definition:Radius of Convergence of Real Power Series/Also known as
- Definition:Radius of Convergence/Complex Domain
- Definition:Radius of Convergence/Real Domain
- Definition:Real Power Series