Category:Weierstrass Function

This category contains results about the Weierstrass function.
Definitions specific to this category can be found in Definitions/Weierstrass Function.

Let $a \in \openint 0 1$.

Let $b$ be a strictly positive odd integer such that:

$\ds a b > 1 + \frac 3 2 \pi$

Let $f: \R \to \R$ be a real function defined by:

$\ds \map f x = \sum_{n \mathop = 0}^\infty a^n \map \cos {b^n \pi x}$

for each $x \in \R$.

We call $f$ a Weierstrass function.