Note: this is somewhat urgent, so if anyone knows anything about it, please help me out.
I'm trying to teach myself the Gamma Function from here:
The Gamma Function
However, I'm a tad confused at some parts.
I don't understand at all how they figured out (derived) the inequality where it says
"A careful analysis of the Gamma function (especially if we notice that is a convex function) yields the inequality"
...and I don't know what a convex function is. I don't really see the significance in deriving the function in all these different ways.
Also, when they give the intial formula, I don't understand how it was derived/where it came from. Does anyone know how it was formulated?
Thanks for all your help.