Difference between revisions of "Faber F1"
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=Properties= | =Properties= | ||
| − | + | [[Faber F1 is continuous]]<br /> | |
| − | + | [[Faber F1 is nowhere differentiable]]<br /> | |
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=See Also= | =See Also= | ||
| − | [[Faber | + | [[Faber F2]] |
=References= | =References= | ||
[https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] | [https://pure.ltu.se/ws/files/30923977/LTU-EX-03320-SE.pdf] | ||
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| + | {{:Continuous nowhere differentiable functions footer}} | ||
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| + | [[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
