Difference between revisions of "Darboux function"
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Revision as of 17:13, 23 June 2016
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
