I'm reading about constant $e$ in textbook Analysis I by Amann/Escher.

I have searched through MSE to found a question containing different ways to calculate $e$. I use such keywords as "constant $e$" and "$e$ identities" but to no avail.

Please help me find such thread! Thank you so much.

  • $\begingroup$ It is true that searching here for something with one letter is difficult. $\endgroup$ – GEdgar Aug 10 '19 at 13:09
  • $\begingroup$ A nice way is to consider the class of (Beukers) integrals $\int_{0}^{1}x^n(1-x)^n e^{-x}\,dx$, which in the long run prove that the continued fraction of $e$ is $$ e=[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,\ldots] $$ Do you need something better than the best rational approximations? :D $\endgroup$ – Jack D'Aurizio Aug 29 '19 at 0:37

https://math.stackexchange.com/search?q=%5Bbig-list%5D+e But to be clear these are questions not threads.

  • $\begingroup$ This has a lot of matches... Any big list with $e^x$ in it, for example. $\endgroup$ – GEdgar Aug 10 '19 at 13:13
  • $\begingroup$ well that is why the big list tag exists to put a lot on a topic in one place. $\endgroup$ – Roddy MacPhee Aug 26 '19 at 12:22

Computing the constant $e$ is closely related to evaluating the exponential function, or its inverse the natural logarithm. If such approaches are of interest to you, try searching for "compute [exponential-function]" or "calculate [logarithms]", etc.

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