[VA] SRC #009 - Pi Day 2021 Special

[J-F Garnier]

(03-16-2021 10:29 PM)Gerson W. Barbosa Wrote:  

(03-15-2021 08:59 PM)J-F Garnier Wrote:  I don't know -and don't think there is - any relation that can be used to get \(\pi\) from e.

Et pourtant, il y en a – and yet there is at least one:

http://oeis.org/wiki/A_remarkable_formula_of_Ramanujan

Really remarkable, isn’t it?

P.S.: Yet another one (I had forgotten about the Gaussian Integral)

\[{\int_{-\infty}^{ \infty}\rm{e}^{-{{x}}^{2}}\rm{d}x}=\sqrt{\pi}\]

OK, I see what you (and Valentin probably too) mean and I agree of course.
By relation, I was (wrongly) limiting myself to finite expressions, like the arctan expression in Valentin's post. There are obviously many infinite sums and integrals involving e and producing pi in a way or another.

J-F