Van der Waerden function

From specialfunctionswiki
Jump to: navigation, search

The van der Waerden function $V \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined by the formula $$V(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{\mathrm{dist}_{\mathbb{Z}} \left(10^k x \right)}{10^k},$$ where $\mathrm{dist}_{\mathbb{Z}}$ denotes the distance to integers function.


Properties[edit]

van der Waerden function is continuous
van der Waerden function is nowhere differentiable

See Also[edit]

Takagi function

References[edit]

[1]

Continuous nowhere differentiable functions