Difference between revisions of "Cellérier function"

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Let $a>1000$. The Cellérier function is defined as  
 
Let $a>1000$. The Cellérier function is defined as  
$$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x).$$
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$$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$
  
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=Properties=
<strong>Theorem:</strong> The Cellérier function is [[continuous]].
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[[Cellérier function is continuous]]<br />
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[[Cellérier function is nowhere differentiable]]<br />
<strong>Proof:</strong>
 
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<strong>Theorem:</strong> The Cellérier function is [[nowhere differentiable]].
 
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<strong>Proof:</strong> █
 
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=References=
 
=References=
 
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] <br />
 
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] <br />
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[[Category:SpecialFunction]]

Latest revision as of 17:11, 23 June 2016

Let $a>1000$. The Cellérier function is defined as $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$

Properties

Cellérier function is continuous
Cellérier function is nowhere differentiable

References

[1]