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

[tex]\Gamma(xy)[/tex]

i tried the following :

[tex]\Gamma(xy)=\int^{\infty}_{0} t^{xy-1} e^{-t} dt[/tex]

now let [tex]t^x = s[/tex]

=> ( after some manipulation )

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

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

[tex]\Gamma(xy)[/tex]

i tried the following :

[tex]\Gamma(xy)=\int^{\infty}_{0} t^{xy-1} e^{-t} dt[/tex]

now let [tex]t^x = s[/tex]

=> ( after some manipulation )

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

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

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