-function
Let be a lattice on . The Weierstrass function associated to is given by
The function is meromorphic and analytic on , whereas at each , it has an order pole. It is also an even function, because .
Its derivative
is also an odd, meromorphic, and elliptic function, analytic at and having order poles at each .
The functions and form together a generator set for the field of elliptic functions associated to the lattice .