# Math Help - about gamma function

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 ..

2. 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 ........