Darboux function

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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.

Properties[edit]

Darboux function is continuous
Darboux function is nowhere differentiable

References[edit]

Continuous nowhere differentiable functions