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 …

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, …

Oct 19, 2016 · 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.

Apr 21, 2015 · Factorial, but with addition [duplicate] Ask Question Asked 11 years, 11 months ago Modified 6 years, 3 months ago

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 …

The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$. Otherwise this would be restricted to $0 <k < n$. A reason that we do define $0!$ to be …

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 …

Sep 4, 2015 · However, there is a continuous variant of the factorial function called the Gamma function, for which you can take derivatives and evaluate the derivative at integer values.

Jun 5, 2021 · To find the factorial of a number, n n, you need to multiply n n by every number that comes before it. For example, if n= 4 n = 4, then n! = 24 n! = 24 since 4⋅3⋅2⋅1= 24 4 3 2 1 = 24. …

Sep 10, 2020 · As I studied, I found factorials for positive reals and negative fractions. But the integral with which we define factorial falls flat on the negative integers. why is that we can find …