• May 27th 2008, 07:43 PM
mmzaj
what is the simplification of the following expression (in terms of gamma and\or other functions) ?

$\displaystyle \Gamma(xy)$

i tried the following :

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

now let $\displaystyle t^x = s$

=> ( after some manipulation )

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

but here is where i'm stuck .. so any help would be appreciated ..
• May 27th 2008, 10:16 PM
mr fantastic
Quote:

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

$\displaystyle \Gamma(xy)$

i tried the following :

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

now let $\displaystyle t^x = s$

=> ( after some manipulation )

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

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 ........