Difference between revisions of "McCarthy function"
From specialfunctionswiki
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=Properties= | =Properties= | ||
| − | [[McCarthy function is continuous]] | + | [[McCarthy function is continuous]]<br /> |
| − | [[McCarthy function is nowhere differentiable]] | + | [[McCarthy function is nowhere differentiable]]<br /> |
=References= | =References= | ||
Latest revision as of 13:39, 17 November 2016
The McCarthy function $M$ is defined by $$M(x) = \displaystyle\sum_{k=1}^{\infty} \dfrac{1}{2^k} g \left( 2^{2^k} x \right),$$ where $$g(x) = \left\{ \begin{array}{ll} 1+x &; x \in [-2,0] \\ 1-x &; x \in [0,2], \end{array} \right.$$ and $g(x+4)=g(x)$ for any $x \in \mathbb{R}$.
Properties
McCarthy function is continuous
McCarthy function is nowhere differentiable
