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, …

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 …

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 …

Apr 21, 2015 · 106 This question already has answers here: What is the term for a factorial type operation, but with summation instead of products? (4 answers)

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.

Feb 6, 2021 · One definition of the factorial that is more general than the usual $$ N! = N\cdot (N-1) \dots 1 $$ is via the gamma function, where $$ \Gamma (N) = (N-1)! = \int_0^ {\infty} x^ {N …

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. …

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 …