Darboux function
From specialfunctionswiki
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.
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
