# Category:Periodic Functions

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This category contains results about **Periodic Functions**.

Definitions specific to this category can be found in Definitions/Periodic Functions.

### Periodic Real Function

Let $f: \R \to \R$ be a real function.

Then $f$ is **periodic** if and only if:

- $\exists L \in \R_{\ne 0}: \forall x \in \R: \map f x = \map f {x + L}$

### Periodic Complex Function

Let $f: \C \to \C$ be a complex function.

Then $f$ is **periodic** if and only if:

- $\exists L \in \C_{\ne 0}: \forall x \in \C: \map f x = \map f {x + L}$

## Subcategories

This category has the following 4 subcategories, out of 4 total.

## Pages in category "Periodic Functions"

The following 19 pages are in this category, out of 19 total.

### D

### P

- Period of Real Cosine Function
- Period of Real Sine Function
- Periodic Element is Multiple of Period
- Periodic Function as Mapping from Unit Circle
- Periodic Function as Mapping from Unit Circle/Motivation
- Periodic Function is Continuous iff Mapping from Unit Circle is Continuous
- Periodic Function plus Constant
- Primitive of Periodic Real Function