Question Number 216906 by MrGaster last updated on 24/Feb/25
![Prove:Γ(x)=(x^x /((2π)^(x−1) ))Π_(k=1) ^∞ (k^(2(x−1)) /(Π_(i=1) ^(x−1) [k^2 −((i/2))^2 ]))](Q216906.png)
$$\mathrm{Prove}:\Gamma\left({x}\right)=\frac{{x}^{{x}} }{\left(\mathrm{2}\pi\right)^{{x}−\mathrm{1}} }\underset{{k}=\mathrm{1}} {\overset{\infty} {\prod}}\frac{{k}^{\mathrm{2}\left({x}−\mathrm{1}\right)} }{\underset{{i}=\mathrm{1}} {\overset{{x}−\mathrm{1}} {\prod}}\left[{k}^{\mathrm{2}} −\left(\frac{{i}}{\mathrm{2}}\right)^{\mathrm{2}} \right]} \\ $$