# Category:Power Series

This category contains results about Power Series.

Definitions specific to this category can be found in Definitions/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 $\xi$**.

## Subcategories

This category has the following 9 subcategories, out of 9 total.

### C

### D

### E

### G

### R

### T

## Pages in category "Power Series"

The following 17 pages are in this category, out of 17 total.

### D

### P

- Partial Sums of Power Series with Fibonacci Coefficients
- Power Series Converges to Continuous Function
- Power Series Converges Uniformly within Radius of Convergence
- Power Series is Differentiable on Interval of Convergence
- Power Series is Taylor Series
- Power Series is Termwise Differentiable within Radius of Convergence
- Power Series is Termwise Integrable within Radius of Convergence