Difference between revisions of "Darboux function"
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where $\sin$ denotes the [[sine]] function. | where $\sin$ denotes the [[sine]] function. | ||
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| − | < | + | File:Darbouxplot.png|Plot of $D(x)$ on $[0,5]$. |
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| − | + | =Properties= | |
| − | < | + | [[Darboux function is continuous]]<br /> |
| − | + | [[Darboux function is nowhere differentiable]]<br /> | |
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=References= | =References= | ||
| − | [ | + | * {{BookReference|Continuous Nowhere Differentiable Functions|2003|Johan Thim|prev=findme|next=Schwarz function}} $\S 3.5$, pg. 28 |
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| + | {{:Continuous nowhere differentiable functions footer}} | ||
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| + | [[Category:SpecialFunction]] | ||
Latest revision as of 18:02, 25 June 2017
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
