Recent searches
Search options
@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:
@robinhouston - an amusing fact: in 1995, in a paper on the arXiv, Kent Morrison said "we might conjecture" that
Both these are false, of course! I read about this here:
MathOverflowA conjecture on integrals of infinite productsThe problem I would like to discuss in this post is about a conjecture on the following integrals,
\begin{align}
\int_0^\infty \prod_{n=1}^\infty \cos(x/n)\,dx \stackrel{?}= \pi/4 \tag{1}\\
\int_0^...
@AndresCaicedo - I don't go around saying that to everyone. But Robin and I have been talking about the failure of these identities for days now. There are papers about them, and whole web page about them:
https://mathworld.wolfram.com/InfiniteCosineProductIntegral.html
mathworld.wolfram.comSOHCAHTOA -- from Wolfram MathWorld"SOHCAHTOA" is a helpful mnemonic for remembering the definitions of the trigonometric functions sine, cosine, and tangent i.e., sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent, sintheta = (opposite)/(hypotenuse) (1) costheta = (adjacent)/(hypotenuse) (2) tantheta = (opposite)/(adjacent). (3) Other mnemonics include 1. "Tommy On A Ship Of His Caught A Herring" (probably more common in Great...