# Weierstrass elliptic function

## Class of mathematical functions / From Wikipedia, the free encyclopedia

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"P-function" redirects here. For the phase-space function representing a quantum state, see Glauber–Sudarshan P representation.

"℘" redirects here; the symbol can also be used to denote a power set.

In mathematics, the **Weierstrass elliptic functions** are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as **℘-functions** and they are usually denoted by the symbol ℘, a uniquely fancy script *p*. They play an important role in the theory of elliptic functions, i.e., meromorphic functions that are doubly periodic. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.