Difference between revisions of "Darboux function"

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=References=
 
=References=
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf]<br />
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* {{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}}
  
 
[[Category:SpecialFunction]]
 
[[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.

Properties

Darboux function is continuous
Darboux function is nowhere differentiable

References

Continuous nowhere differentiable functions