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How do you do this?

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- Mar 13th 2009, 08:06 PMVkLIntegral Question
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How do you do this? - Mar 13th 2009, 08:08 PMo_O
- Mar 13th 2009, 10:40 PMmatheagle
That's the definition of the Gamma function...

$\displaystyle \Gamma (a)=\int_0^{\infty} t^{a-1} e^{-t} dt$.

for a>0. The first thing you learn about this function is that

$\displaystyle \Gamma (a)=(a-1)\Gamma (a-1)$ and it's easy to show that

$\displaystyle \Gamma (1)=1$. Thus $\displaystyle \Gamma (2)=1$...., whence $\displaystyle \Gamma (n)=(n-1)!$ where n is an integer.