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?.
Why is this? I know what a factorial is, so what does it actually mean to take the factorial of a complex number? Also, are those parts of the complex answer rational or irrational? Do complex factorials give rise to any interesting geometric shapes/curves on the complex plane?
Some theorems that suggest that the Gamma Function is the "right" extension of the factorial to the complex plane are the Bohr–Mollerup theorem and the Wielandt theorem.
I was playing with my calculator when I tried $1.5!$. It came out to be $1.32934038817$. Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\times1$, but how do we e...
Closed 12 years ago. Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the factorial $5!$ way. EDIT: I know about the formula. I want to know if there's a short notation.
But, Desmos is able to calculate factorial of floating point values such as $0.1 , 0.2 , 0.3, 0.4$ etc. I'm aware of gamma function but not well verse will integrals ...
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?