Definition:Periodic Function
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Definition
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:
- $\exists L \in \C_{\ne 0}: \forall x \in \C: \map f x = \map f {x + L}$
Periodic Element
Let $L \in X_{\ne 0}$.
Then $L$ is a periodic element of $f$ if and only if:
- $\forall x \in X: \map f x = \map f {x + L}$
Also see
- General Periodicity Property: after every distance $L$, the function $f$ repeats itself.
- Results about periodic functions can be found here.