# Thread: the min. value of gamma function

1. ## 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 $\int_0^{\infty} e^{-t} \ln(t) t^{x-1}~ dt~ = 0$?

2. Originally Posted by simplependulum
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 $\Gamma(x_{\min})$.