I am wondering how the following statement holds true:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Gamma\left(\frac{1}{2}\right)=\int_0^{\infty}e^{-x}x^{-\frac{1}{2}}\,dx=\sqrt{\pi}[/tex]

I know how to show that:

[tex]\int_0^{\infty}e^{-x^2}\,dx=\frac{\sqrt{\pi}}{2}[/tex]

But I can't seem to apply that method (converting to a double-integral) to the gamma function. Any ideas?

Thanks.

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# Homework Help: Gamma Function

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