[itex]\Gamma[/itex](n) = int(0 to infinity)[(x^(n-1))*e^-x]dx(adsbygoogle = window.adsbygoogle || []).push({});

Show that it can also be written as:

[itex]\Gamma[/itex](n) = 2int(0 to infinity)[(x^(2n-1))*e^(-x^2)]dx

I have no idea how to go about this. I have tried integration by parts of each to see if anything relates, but how can you get from an exp(-x) to and exp(-x^2) term?

Any help would be appreciated.

(PS apologies, I am unfamiliar with writing formulae using latex)

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# How do you derive this alternate form of the gamma function?

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