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, …

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 …

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

Feb 6, 2021 · If you are starting from the "usual" definition of the factorial, in my opinion it is best to take the statement $0! = 1$ as a part of the definition of the factorial function, as anything …

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 …

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 …

Jun 29, 2015 · 12 I've been searching the internet for quite a while now to find anything useful that could help me to figure out how to calculate factorial of a certain number without using …

Jun 5, 2021 · As mentioned by Joe in the comments, Stirling's approximation is a good method to approximate the value of a large factorial, and by rewriting the factorial as a Gamma function, …