I created a conjecture.
I did not try to prove it, but I want to see how it works in Matlab.
Conjecture: Let G(x) represent the Gamma function. Then if x1,x2,x3,...,xn are real numbers above 1 (including 1) we have that,
[G(x1+x2+...+xn)]^n <= G(n*x1)*G(n*x2)*...*G(n*xn)
Note: I have been able to prove if for n=2 (problem of the week).
I am hoping to first prove n=3 before attempting the generalized case. The good thing is that you can plot this in MatLab because it is a 3-dimensional graph. But you cannot above that. See if you can do that for n=3. Just be careful it does not overload the CPU!
One more note, equality only occurs when all are equal.