Weierstrass nowhere differentiable function

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The Weierstrass function is $$f(x)=\displaystyle\sum_{k=0}^{\infty} a^k \cos(b^k\pi x),$$ where $0<a<1$ and $b \in \{1,3,5,7,9,\ldots\}$ such that $ab > 1+\dfrac{3}{2}\pi$.

Properties[edit]

Weierstrass function is continuous
Weierstrass function is nowhere differentiable

Videos[edit]

Weierstrass example (17 October 2013)

References[edit]

[1]