Question Number 141322 by mnjuly1970 last updated on 17/May/21
$$\:\:\:\:\:……{advanced}……..{calculus}……. \\ $$$$\:{prove}\:{that}:: \\ $$$$\:\:\:\xi:=\underset{{n}=\mathrm{2}} {\overset{\infty} {\prod}}{e}\left(\mathrm{1}−\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\right)^{{n}^{\mathrm{2}} } =\frac{\pi}{{e}\sqrt{{e}}} \\ $$$$ \\ $$