about gamma function

**mmzaj** · May 27th 2008, 07:43 PM

what is the simplification of the following expression (in terms of gamma and\or other functions) ?

$\Gamma(xy)$

i tried the following :

$\Gamma(xy)=\int^{\infty}_{0} t^{xy-1} e^{-t} dt$

now let $t^x = s$

=> ( after some manipulation )

$\Gamma(xy)=\frac{1}{x}\int^{\infty}_{0} s^{y-1} exp{-s^\frac{1}{x}} ds$

but here is where i'm stuck .. so any help would be appreciated ..

**mr fantastic** · May 27th 2008, 10:16 PM

Originally Posted by mmzaj

what is the simplification of the following expression (in terms of gamma and\or other functions) ?

$\Gamma(xy)$

i tried the following :

$\Gamma(xy)=\int^{\infty}_{0} t^{xy-1} e^{-t} dt$

now let $t^x = s$

=> ( after some manipulation )

$\Gamma(xy)=\frac{1}{x}\int^{\infty}_{0} s^{y-1} exp{-s^\frac{1}{x}} ds$

but here is where i'm stuck .. so any help would be appreciated ..

Perhaps an 'easier' problem to first consider would be the simplification of (nm)! where n and m are non-negative integers ........

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