Difference between revisions of "Cellérier function"
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(Created page with "Let $a>1000$. The Cellérier function is defined as $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x).$$ <div class="toccolours mw-collapsible mw-colla...") |
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Let $a>1000$. The Cellérier function is defined as | Let $a>1000$. The Cellérier function is defined as | ||
| − | $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x).$$ | + | $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$ |
<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
Revision as of 22:46, 31 December 2015
Let $a>1000$. The Cellérier function is defined as $$C(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{a^k} \sin\left(a^k x \right).$$
Theorem: The Cellérier function is continuous.
Proof: █
Theorem: The Cellérier function is nowhere differentiable.
Proof: █
