Fonction sigma de weierstrass biography

Mathematical functions related to Weierstrass's elliptic function

For the fractal continuous function without a defined derivative, see Weierstrass function.

In mathematics, the Weierstrass functions are special functions of a complex variable that are auxiliary to the Weierstrass elliptic function.

They are named for Karl Weierstrass. The relation between the sigma, zeta, and functions is analogous to that between the sine, cotangent, and squared cosecant functions: the logarithmic derivative of the sine is the cotangent, whose derivative is negative the squared cosecant.

Weierstrass sigma function

The Weierstrass sigma function associated to a two-dimensional lattice is defined to be the product

where denotes or are a fundamental pair of periods.

Through careful manipulation of the Weierstrass factorization theorem as it relates also to the sine function, another potentially more manageable infinite product definition is

for an