Category:Definitions/Periodic Functions

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This category contains definitions related to Periodic Functions.
Related results can be found in Category: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:

$\exists L \in \C_{\ne 0}: \forall x \in \C: f \left({x}\right) = f \left({x + L}\right)$