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In this German Mathematics Wikibook page, formula $0.5$ lists the following equation $$\int_0^1 \sin(\pi x) x^x (1-x)^{1-x} \ \mathrm{d}x = \frac{\pi e}{24}$$ as supposedly attributed to Ramanujan (Google translate gives "formula by Ramanujan"). However, the page lacks a citation section, which is absolutely unfortunate, so I'm not certain whether to trust this source or not. How would I be able to verify the source is correct?

A quick Google search only returned the above the page, so no promising results. I have thought about contacting Dr. Bruce C. Berndt, the expert on Ramanujan's mathematical career, though I'd like to know what other alternatives are available. Thank you!

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    $\begingroup$ Did you ask Tobias Pfanner (the author of the Wikibooks page)? $\endgroup$
    – Emil Jeřábek
    Commented Jun 15, 2016 at 16:06
  • $\begingroup$ I am not familiar with him. Where would I be able to find his contact information? I would assume he would also be an administrator of the site listed above, though I am not finding his name. $\endgroup$
    – Brian
    Commented Jun 15, 2016 at 16:40
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    $\begingroup$ Math.SE: Prove that $\int_{0}^{1}\sin{(\pi x)}x^x(1-x)^{1-x}\,dx =\frac{\pi e}{24} $. BTW it was the first result when I searched for frac pi e 24 integral in Google. $\endgroup$
    – Martin Sleziak
    Commented Jun 15, 2016 at 16:47
  • $\begingroup$ Each Mediawiki page has an edit history (in German, it’s the link called “Versionsgeschichte”). There you can find what edits were done by what users; in this case, it’s pretty much a one-man job. Next to each user name, there is a link to their user talk page (“Diskussion”), here de.wikibooks.org/wiki/Benutzer_Diskussion:Tobias_Pfanner . You can ask a question there. However, the user seems not to have been active for some time, so it’s unclear whether that will work. $\endgroup$
    – Emil Jeřábek
    Commented Jun 15, 2016 at 16:47
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    $\begingroup$ Just to clarify - since the page you linked has a proof of this result, you are probably not asking for a proof, but rather for a reference containing this result? If that's the case, you should probably use (reference-request) tag. (And make this clear in the post.) $\endgroup$
    – Martin Sleziak
    Commented Jun 15, 2016 at 16:52

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