Cellérier function

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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[edit]

Cellérier function is continuous
Cellérier function is nowhere differentiable

References[edit]

[1]