Definition:Weierstrass Function/Historical Note

Historical Note on Weierstrass Function
first discussed a real function which was continuous everywhere but differentiable nowhere in his lectures in $1861$.

The function he initially demonstrated was defined as the sum of a Fourier Series:


 * $\displaystyle f \left({x}\right) = \sum_{n \mathop \ge 0} a^n \cos \left({b^n \pi x}\right)$

where:
 * $0 < a < 1$
 * $b$ is a (strictly) positive odd integer

such that:
 * $a b > 1 + \dfrac 3 2 \pi$

It did not appear in print until one of his students published it (with 's permission) in $1874$.