Definition:Antiperiodic Function/Complex

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

Then $f$ is anti-periodic if and only if:

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


The antiperiod of $f$ is the smallest value $\cmod L \in \R_{\ne 0}$ such that:

$\forall x \in X: - \map f x = \map f {x + L}$

where $\cmod L$ is the modulus of $L$.

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