Difference between revisions of "Faber F1"
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(Created page with "The Faber functions are $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|$$ and $$F_2(x)=\displaystyle\...") |
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| − | The Faber | + | The Faber function $F_1$ is defined by |
| − | $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|$$ | + | $$F_1(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{10^k} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!} x -m \right|.$$ |
| − | + | ||
| − | $$ | + | <div align="center"> |
| + | <gallery> | ||
| + | File:Faberf1plot.png|Plot of $F_1$. | ||
| + | </gallery> | ||
| + | </div> | ||
| + | |||
| + | =Properties= | ||
| + | [[Faber F1 is continuous]]<br /> | ||
| + | [[Faber F1 is nowhere differentiable]]<br /> | ||
| + | |||
| + | =See Also= | ||
| + | [[Faber F2]] | ||
| + | |||
| + | =References= | ||
| + | [https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] | ||
| + | |||
| + | {{:Continuous nowhere differentiable functions footer}} | ||
| + | |||
| + | [[Category:SpecialFunction]] | ||
Latest revision as of 03:32, 6 July 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 F1 is nowhere differentiable
