Interesting read

I've worked with those functions for school for like 2 years now

I couldn't resist looking things up on Wolfram Alpha with what you said.
It turns out that :

(

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I wanted to graph the difference between the 2 things :
It's commonly known that gamma(x+1) == x!, so graphing what you say is (to see the difference) :

A bit weird (against your idea at least) since it doesn't look like it's converging as x gets bigger ?....
But then I saw that W|A actually give what you'd be looking for : the difference between the 2 expressions :

But that's not really usable then ^^
(Well, Mathematice 9 doesn't get further, or at least not directly :

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