[tex]\Gamma(x)=\int^{\infty}_0t^{x-1}e^{-t}dt[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma(\frac{1}{2})=\int^{\infty}_0\frac{e^{-t}}{\sqrt{t}}dt=[/tex]

take [tex]t=x^2[/tex]

[tex]dt=2xdx[/tex]

[tex]x=\sqrt{t}[/tex]

[tex]=\int^{\infty}_0\frac{e^{-x^2}}{x}2xdx[/tex]

Why here we can here reducing integrand by [tex]x[/tex]?

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# Gamma function calculation

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