Let L be a lattice on . The Weierstrass functionMathworldPlanetmath associated to L is given by


The function is meromorphic and analytic on L, whereas at each wL, it has an order 2 pole. It is also an even functionMathworldPlanetmath, because (z)=(-z).

Its derivative


is also an odd, meromorphic, and elliptic functionMathworldPlanetmath, analytic at L and having order 3 poles at each wL.

The functions and form together a generator set for the field of elliptic functions associated to the lattice L.

Title -function
Canonical name wpfunction
Date of creation 2013-03-22 14:51:54
Last modified on 2013-03-22 14:51:54
Owner drini (3)
Last modified by drini (3)
Numerical id 10
Author drini (3)
Entry type Definition
Classification msc 33E05
Synonym Weierstrass function
Synonym Weierstrass p-function
Synonym p-Weierstrass
Synonym Weierstrass -function
Related topic EllipticCurve
Related topic EllipticFunction
Related topic ExamplesOfEllipticFunctions