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.

Why is the factorial of zero, one. What is the mathematical proof behind 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 …

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)

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 …

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 …

3 days ago · My guess of why this totient-bypass relationship exists by virtue of factorial(n) having comprehensive coverage of everything up to n, thus totient of individual prime factors would …

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 …