In mathematics, the Weierstrass function was the first example found of a function with the property that it is continuous everywhere but differentiable nowhere. The Weierstrass function is defined by
f ( x ) = ∑ n = 0 ∞ a n cos ( b n π x ) , {\displaystyle f(x)=\sum _{n=0}^{\infty }a^{n}\cos(b^{n}\pi x),}
where 0 < a < 1 {\displaystyle 0<a<1} and
The following graphs displays the function f ( x ) = ∑ n = 0 ∞ ( 1 / 2 ) n cos ( 20 n π x ) , {\displaystyle f(x)=\sum _{n=0}^{\infty }(1/2)^{n}\cos(20^{n}\pi x),}
File:Weierfunc1.gif File:Weierfunc2.gif
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