ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F12499 on D1583: Weierstrass function
F12499
Formulation 1
Let $a \in (0, 1)$ be a D5407: Positive real number such that
(i) $b \in 2 \mathbb{Z} + 1$ is an D7: Odd integer
(ii) \begin{equation} a b > 1 + \frac{3 \pi}{2} \end{equation}
The Weierstrass function with respect to $(a, b)$ is the D4364: Real function \begin{equation} \mathbb{R} \to \mathbb{R}, \quad x \mapsto \sum_{n = 0}^{\infty} a^n \cos(b^n \pi x) \end{equation}