Darboux function

The Darboux function is defined by $$D(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{\sin\left((k+1)!x\right)}{k!},$$ where $\sin$ denotes the sine function.

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  Plot of $D(x)$ on $[0,5]$.

Properties

Darboux function is continuous
Darboux function is nowhere differentiable

References

• 2003: Johan Thim: Continuous Nowhere Differentiable Functions ... (previous) ... (next) $\S 3.5$, pg. 28

Continuous nowhere differentiable functions

Darboux function

Faber F1

Faber F2

Takagi

van der Waerden