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In mathematics, the Weierstrass function was the first example found of a kind of function with the property that it is continuous everywhere but differentiable nowhere. Almost all continuous functions are nowhere differentiable, and this property is both stable and generic. Weierstrass functions are defined by
<math>f(x)=\sum_{n=0}^\infty a^n\cos(b^n\pi x),<math>
where <math>0
- <math> ab>1+\frac{3}{2}\pi.<math>
The following graphs display the function <math>f(x)=\sum_{n=0}^\infty (1/2)^n\cos(20^n\pi x),<math>
See also
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