# Threads containing different ways to calculate $e$

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.

• It is true that searching here for something with one letter is difficult. – GEdgar Aug 10 '19 at 13:09
• 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 – Jack D'Aurizio Aug 29 '19 at 0:37

• This has a lot of matches... Any big list with $e^x$ in it, for example. – GEdgar Aug 10 '19 at 13:13
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.