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Author: Zbigniew Fiedorowicz
Created in Microsoft Excel and Maple
An approximation to the graph of a pathological, highly non-continuous function, which nevertheless has an w:antiderivative (Example 4). The parametric equation for this graph is

${\displaystyle t\mapsto \left(\sum _{n=1}^{8}{\frac {(t-\cos(n))^{1/3}}{2^{n}}},{\frac {1}{\sum _{n=1}^{8}{\frac {(t-\cos(n))^{-2/3}}{3\cdot 2^{n}}}}}\right)}$

where ${\displaystyle -1\leq t\leq 1}$ and where ${\displaystyle {\frac {1}{\sum _{n=1}^{8}{\frac {(t-\cos(n))^{-2/3}}{3\cdot 2^{n}}}}}}$ is taken to be 0 for ${\displaystyle t=\cos(1),\cos(2),\dots ,\cos(8)}$. In the actual example, 8 in the upper limit of summation should be replaced by ${\displaystyle \infty }$.

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• (del) (cur) 16:38, 13 December 2005 . . Fiedorow ( en:User_talk:Fiedorow Talk) . . 483x483 (8708 bytes) (== Summary == Author: Zbigniew Fiedorowicz<br> Created in Microsoft Excel and Maple<br> An approximation to the graph of a pathological, highly non-continuous function, which nevertheless has an en:Antiderivative antiderivative (Example 4). The parametric equation for )
• (del) (rev) 03:45, 11 December 2005 . . Fiedorow ( en:User_talk:Fiedorow Talk) . . 205x151 (3564 bytes) (Author: Zbigniew Fiedorowicz Created in Microsoft Excel and Paint Shop Pro )

en:Image:Antideriv1.gif