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Question-107621




Question Number 107621 by mathdave last updated on 11/Aug/20
Commented by john santu last updated on 12/Aug/20
Γ(2x) = ((4^x  Γ(x) Γ(x+(1/2)))/(2(√π))) .   put x = (n/4)  Γ((n/2)) = ((4^(n/4) Γ((n/4))Γ((n/4)+(1/2)))/(2(√π)))   ...
$$\Gamma\left(\mathrm{2}{x}\right)\:=\:\frac{\mathrm{4}^{{x}} \:\Gamma\left({x}\right)\:\Gamma\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\:.\: \\ $$$${put}\:{x}\:=\:\frac{{n}}{\mathrm{4}} \\ $$$$\Gamma\left(\frac{{n}}{\mathrm{2}}\right)\:=\:\frac{\mathrm{4}^{\frac{{n}}{\mathrm{4}}} \Gamma\left(\frac{{n}}{\mathrm{4}}\right)\Gamma\left(\frac{{n}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\right)}{\mathrm{2}\sqrt{\pi}}\: \\ $$$$… \\ $$

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