Question Number 126323 by mnjuly1970 last updated on 19/Dec/20
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:\:{prove}\:\:\:{that}\:::: \\ $$$$\:\:\:\:\:\frac{\Gamma\left(\frac{\mathrm{1}−{x}}{\mathrm{2}}\right)\Gamma\left({x}\right)}{\Gamma\left(\frac{{x}}{\mathrm{2}}\right)}\:\overset{???} {=}\:\frac{\mathrm{2}^{{x}−\mathrm{1}} \sqrt{\pi}}{{cos}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$$$ \\ $$