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Math Help - about gamma function

  1. #1
    Junior Member
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    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 ..
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  2. #2
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    Quote Originally Posted by mmzaj View Post
    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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