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Math Help - the min. value of gamma function

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    the min. value of gamma function

    What is the min. value of gamma function  \Gamma(x) ~~ x > 0 ?

    How do I start with .. finding zero derivative  \int_0^{\infty} e^{-t} \ln(t) t^{x-1}~ dt~ = 0  ?
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    Quote Originally Posted by simplependulum View Post
    What is the min. value of gamma function  \Gamma(x) ~~ x > 0 ?

    How do I start with .. finding zero derivative  \int_0^{\infty} e^{-t} \ln(t) t^{x-1}~ dt~ = 0  ?
    The answer is given here (without explanantion) as \Gamma(x_{\min}) = 0.885603194410888.... There doesn't seem to be a closed form expression for either x_{\min}\ (= 1.461632144968362341262...) or \Gamma(x_{\min}).
    Last edited by Opalg; August 10th 2009 at 11:31 AM.
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