Definition:Weierstrass Function

Definition
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.

Also see

 * Weierstrass Function is Continuous


 * Weierstrass Function is Nowhere Differentiable


 * Weierstrass's Theorem