Weierstrass functions

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

where denotes .

The Weierstrass zeta function is defined by the sum

The Weierstrass zeta function is the logarithmic derivative of the sigma-function. The zeta function can be rewritten as:

where is the Eisenstein series of weight 2k + 2.

This page was last edited on 28 September 2017, at 12:13.
Reference: https://en.wikipedia.org/wiki/Weierstrass_sigma_function under CC BY-SA license.

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