Cellérier function

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: █

References

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