Talk:Fabius function

When it says "given by the probability distribution", does it mean specifically "given by the cumulative probability distribution function"? And if not, what does it mean? If so, it should say so. Michael Hardy (talk) 04:41, 7 January 2012 (UTC)

I have modified the text accordingly. 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? 73.11.255.69 (talk) 04:58, 14 August 2018 (UTC)


 * Yes, as it stands, it sounds to me like Wikipedia is saying they found it first -- implying that they wrote the formula, proved that it was smooth, AND that it was nowhere-analytic. I had a look at section 8, I don't see anything about nowhere-analytic. --2607:FEA8:86DC:B0C0:F016:A8CE:D915:F366 (talk) 10:24, 23 April 2022 (UTC)

Self-differential function
According to https://people.math.osu.edu/edgar.2/selfdiff/ the Fabius function is a self-differential function. Is this a relevant mathematical notion (I couldn't find an article on that property) that is worth mentioning? Leonry (talk) 08:31, 3 June 2021 (UTC)


 * That’s just someone’s description of the functional differential equation $$f'(x) = 2f(2x)$$. Anders Kaseorg (talk) 06:11, 28 January 2023 (UTC)