It seems that the answer lies within the inverse regularised gamma function, but nowhere that I've checked gives me the actual definition of the function.
Thus far I've found two other (although not terribly useful) possibilities to define the inverse factorial.
1. Divide by consecutive positive integers until you get a non-integer result, or 1. the number you divided by to get one will be the answer.
2. x = y! (Not very useful)
Does anyone have any ideas or info to contribute? _________________ QUICK_EDIT
Joined: 26 Nov 2002 Location: Algae Colony On Mars
Posted: Wed Oct 15, 2008 4:01 pm Post subject:
Factorials aren't like squares and square roots, not every real number can be used in a factorial. The big killer to this is that only a certain subset of real numbers can even have factorials. You can divide each number into its prime factors but that doesn't really get you what you want.
From what I can see of the gamma function (I'm afraid I'm not a mathematician so I can't give a definite answer) it is a generalised form of factorials because it works for all real and complex numbers. However, Γ(4) isn't 4!, it's 3! which makes me think it could possibly be a slightly different function than just merely factorials. If that's the case, the inverse gamma function (which I can't find anything on either) isn't actually giving the factorial. I suggest you find a mathematician and bug them, they're probably more useful and a forum mostly filled with 12-16 year olds and a few university undergraduates plus random others. _________________
Quote:
This is sexier than what this forum was supposed to tolerate. - Banshee
Yeah, that's what I thought. Although, the gamma function of x+1 is equivalent to the factorial function (were it extended to the set of all real numbers). _________________ QUICK_EDIT
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