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 …

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)

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.

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 …

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 …

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 …

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 …

Jun 22, 2018 · what is the value of i factorial? "I" belongs to the complex number system. Thanks for helping me out with this problem.