Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)? Here is an example: 5!...
So, basically, factorial gives us the arrangements. Now, the question is why do we need to know the factorial of a negative number?, let's say -5. How can we imagine that there are -5 seats, and we need to arrange it? Something, which doesn't exist shouldn't have an arrangement right? Can someone please throw some light on it?.
Approximating log of factorial Ask Question Asked 14 years ago Modified 7 years, 11 months ago
The factorial function is only defined on the positive integers, so those don't make sense. However, there is a generalization of the factorial called the Gamma function which you might want to check out.
Infinite series of nth root of n factorial Ask Question Asked 12 years, 2 months ago Modified 6 years, 1 month ago
real analysis - Infinite series of nth root of n factorial ...
It is a valid question to extend the factorial, a function with natural numbers as argument, to larger domains, like real or complex numbers. The gamma function also showed up several times as certain integrals, so mathematicians gave it a name and of course noted the relationship to factorials.
However, this page seems to be saying that you can take the factorial of a fraction, like, for instance, $\frac {1} {2}!$, which they claim is equal to $\frac {1} {2}\sqrt\pi$ due to something called the gamma function. Moreover, they start getting the factorial of negative numbers, like $-\frac {1} {2}! = \sqrt {\pi}$ How is this possible?