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   John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 05-Jan-2023 16:04:00 JST John Carlos Baez

   • robinhouston

   @robinhouston brought this amazing fact to our attention.

   It's been studied by some very smart people, like Borwein and Bailey. It's still mysterious. But we're trying to figure it out here:

   https://mathstodon.xyz/@robinhouston/109622019655110557

   • らりお・ザ・何らかの🈗然㊌ソムリエ repeated this.
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     John Carlos Baez (johncarlosbaez@mathstodon.xyz)'s status on Thursday, 05-Jan-2023 16:04:46 JST John Carlos Baez

     in reply to

     • robinhouston

     @robinhouston - an amusing fact: in 1995, in a paper on the arXiv, Kent Morrison said "we might conjecture" that

     \[
     \int_0^\infty \prod_{n=1}^\infty \cos(x/n)\,dx \stackrel{?}= \pi/4 \]

     \[ \int_0^\infty \cos(2x) \prod_{n=1}^\infty \cos(x/n)\,dx \stackrel{?}= \pi/8 \]

     Both these are false, of course! I read about this here:

     https://mathoverflow.net/q/354932/2893