Riemann function

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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[edit]

Riemann function is continuous
Riemann function is almost nowhere differentiable

References[edit]

[1]