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 …

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 …

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.

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 · 105 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 …

Jul 16, 2020 · @KaviRamaMurthy I feel you are misinterpreting the question. The OP does not appear to be asking how to write n! n! as a polynomial with coefficients being functions of n n, …

I came across a question where I needed to find the sum of the factorials of the first n n numbers. So I was wondering if there is any generic formula for this? Like there is a generic formula for …

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.