Difference between revisions of "Cellérier function"
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$$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$ | $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$ | ||
| − | + | =Properties= | |
| − | + | [[Cellérier function is continuous]]<br /> | |
| − | + | [[Cellérier function is nowhere differentiable]]<br /> | |
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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
