 Weierstrass functions

Associated with a period lattice are the Weierstrass sigma, zeta, eta and elliptic functions. They satisfy $\zeta ={\sigma }^{\prime }/\sigma$ and $\wp =-{\zeta }^{\prime }$; the eta constants record quasi-period increments of the Weierstrass zeta function.

The Weierstrass function is a famous example of a continuous function that is nowhere differentiable. It serves as a significant illustration in real analysis and illustrates properties of functions that may be surprisingly counterintuitive.