Riemann function
From specialfunctionswiki
The Riemann function is the function $R \colon \mathbb{R} \rightarrow \mathbb{R}$ defined by $$R(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin(k^2 x)}{k^2}.$$
Properties
Theorem: The Riemann function is is continuous.
Proof: █
Theorem: The Riemann function is nowhere differentiable except at points of the form $\pi \dfrac{2p+1}{2q+1}$ with $p,q \in \mathbb{Z}$.
Proof: █
