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Summary

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 ${\displaystyle \infty }$.

Licensing

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Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue

Original upload log

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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

Original upload log