Difference between revisions of "Faber F1"
From specialfunctionswiki
| Line 9: | Line 9: | ||
=Properties= | =Properties= | ||
| − | + | [[Faber F1 is continuous]]<br /> | |
| − | + | [[Faber F2 is nowhere differentiable]]<br /> | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | </ | ||
Revision as of 17:15, 23 June 2016
The Faber function $F_1$ is defined by $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|.$$
Plot of $F_1$.
Properties
Faber F1 is continuous
Faber F2 is nowhere differentiable
