Difference between revisions of "Weierstrass nowhere differentiable function"
From specialfunctionswiki
| Line 10: | Line 10: | ||
</div> | </div> | ||
</div> | </div> | ||
| + | |||
| + | =Videos= | ||
| + | [https://www.youtube.com/watch?v=pCEFZk9Vihs Weierstrass example]<br /> | ||
=References= | =References= | ||
Revision as of 21:10, 1 June 2016
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
Theorem: The Weierstrass function $f$ is continuous everywhere but differentiable nowhere.
Proof: █
