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 $1$ is so that …

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, and we …

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 complex factorials …

Dec 14, 2025 · The efficiency was so insane that pre-dropping multiples of 5 ended up slowly things down drastically. So now that I have a good primorial module, if there are further relationships that …

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.

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.

Feb 15, 2014 · I'm not saying a formula for the factorial function cannot be found that is optimal for all x ⩾ 0 x ⩾ 0; I simply have neither the time nor the mathematical expertise to do it myself.

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 …

Nov 28, 2023 · Does this prove that the factorial grows faster than the exponential? Ask Question Asked 2 years, 2 months ago Modified 2 years, 2 months ago

Jul 18, 2023 · How to find the highest power of the divisor of a factorial number [duplicate] Ask Question Asked 2 years, 6 months ago Modified 2 years, 6 months ago