In mathematics, a doubly periodic function is a function defined on the complex plane and having two "periods", which are complex numbers u and v that are linearly independent as vectors over the field of real numbers. That u and v are periods of a function ƒ means that
for all values of the complex number z.[1][2]
The doubly periodic function is thus a two-dimensional extension of the simpler singly periodic function, which repeats itself in a single dimension. Familiar examples of functions with a single period on the real number line include the trigonometric functions like cosine and sine, In the complex plane the exponential function ez is a singly periodic function, with period 2πi.
^"Double-periodic function", Encyclopedia of Mathematics, EMS Press, 2001 [1994], adapted from an original article by E.D. Solomentsev.
^Weisstein, Eric W. "Doubly Periodic Function". mathworld.wolfram.com. Wolfram Mathworld. Retrieved 3 October 2022.
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