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Question Number 163346 by MathsFan last updated on 06/Jan/22
how do i calculate for (1/2)!
$${how}\:{do}\:{i}\:{calculate}\:{for}\:\frac{\mathrm{1}}{\mathrm{2}}! \\ $$
Commented by Ar Brandon last updated on 06/Jan/22
Γ(x+1)=xΓ(x)=x(x−1)Γ(x−1)...Γ(1)=x!  Γ((1/2))=(√π)  ,  Γ(1)=1  ((1/2))!=Γ((1/2)+1)=(1/2)Γ((1/2))=((√π)/2)
$$\Gamma\left({x}+\mathrm{1}\right)={x}\Gamma\left({x}\right)={x}\left({x}−\mathrm{1}\right)\Gamma\left({x}−\mathrm{1}\right)…\Gamma\left(\mathrm{1}\right)={x}! \\ $$$$\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\sqrt{\pi}\:\:,\:\:\Gamma\left(\mathrm{1}\right)=\mathrm{1} \\ $$$$\left(\frac{\mathrm{1}}{\mathrm{2}}\right)!=\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}+\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{2}}\Gamma\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=\frac{\sqrt{\pi}}{\mathrm{2}} \\ $$
Commented by MathsFan last updated on 06/Jan/22
merci
$${merci} \\ $$

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