Faber F2

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The Faber function $F_2$ is defined by $$F_2(x)=\displaystyle\sum_{k=1}^{\infty} \dfrac{1}{k!} \displaystyle\inf_{m \in \mathbb{Z}} \left|2^{k!}x-m \right|.$$

Properties

Theorem: The Faber function $F_2$ is continuous.

Proof:

Theorem: The Faber function $F_2$ is nowhere differentiable.

Proof:

See Also

Faber function F1

References

[1]