Talk:Fabius function: Difference between revisions

Revision as of 21:10, 3 October 2017

Revision as of 04:58, 14 August 2018

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I have modified the text accordingly. [[User:MaigoAkisame|MaigoAkisame]] ([[User talk:MaigoAkisame|talk]]) 21:10, 3 October 2017 (UTC)

The Jessen--Wintner reference seems to have some issues. The paper is a dense 40 pages and I didn't find the stated formula anywhere. Somewhat similar formulas do appear, as in Example 3 in Section 6. Ignoring whatever they wrote for a moment, it's pretty obvious that the characteristic function in question is the product of sinc functions (up to a phase shift, right?), and from there we can use that the sinc function can be written as a product of cosines. So, I believe the formula on this page (maybe up to a phase shift or something similarly minor), but it seems wrong-headed in multiple ways: it doesn't seem to actually be in the cited document, and it uses an extra layer of indirection (cosines instead of sincs) for no discernable reason. The Jessen--Wintner reference is clearly at least somewhat relevant around section 8 where they discuss some C^\infty results, though the current way it's written to me implies Jessen--Wintner more or less wrote down Fabius' counterexample 20 years earlier, which doesn't seem at all to be the case. Am I missing something? [[Special:Contributions/73.11.255.69|73.11.255.69]] ([[User talk:73.11.255.69|talk]]) 04:58, 14 August 2018 (UTC)