Definition:Doubly Periodic Function
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Definition
Let $f: \C \to \C$ be a complex function.
Then $f$ is a doubly-periodic function if and only if there exist $\omega_1, \omega_2 \in \C$ such that:
- $(1): \quad \omega_1, \omega_2 \ne 0$
- $(2): \quad \dfrac {\omega_1} {\omega_2} \notin \R$
- $(3): \quad \forall z \in \C: \map f z = \map f {z + \omega_1} = \map f {z + \omega_2}$
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$)