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.
For example, assume that the periods are 1 and i, so that the repeating lattice is the set of unit squares with vertices at the Gaussian integers.
In other words, we can think of the plane and its associated functional values as remaining fixed, and mentally translate the lattice to gain insight into the function's characteristics.