I was on this wikipedia page https://en.wikipedia.org/wiki/List_of_representations_of_e which has a list of representations of the constant e. I came across this one representation that looked interesting and stood out from all of the other ones because it had the cosine function while most others used a factorial:

$e = \left [ -\frac{12}{\pi^2} \sum_{k=1}^\infty \frac{1}{k^2} \ \cos \left ( \frac{9}{k\pi+\sqrt{k^2\pi^2-9}} \right ) \right ]^{-1/3} $

Does anyone know where this formula comes from (ie. who derived it and how they derived it)? Also I understand that e and pi are related through ruler's formula and in complex analysis in general, but this equation seems to not involve complex analysis at all, so why would e, pi, and cosine be related here?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.