Apr 21, 2015 · Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use …

$\begingroup$ 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

$\begingroup$ @PeterTamaroff: The OP asked, "what does it actually mean to take the factorial of a complex number?" And this answer helpfully but tersely says that one way to extend …

Nov 29, 2021 · For example: the factorial of zero i.e. an empty set ( doesn't occur) is 1. As the empty set can be arranged only in 1 way - i.e. by filling nothing. Now, let's take an example: 5 …

The Factorial of a Rational number is defined by the Gamma function. A link is in the comments. Since,

The gamma function, shown with a Greek capital gamma $\Gamma$, is a function that extends the factorial function to all real numbers, except to the negative integers and zero, for which it …

Jun 5, 2021 · As mentioned by Joe in the comments, Stirling's approximation is a good method to approximate the value of a large factorial, and by rewriting the factorial as a Gamma function, …

Oct 19, 2016 · $\begingroup$ 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 …

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 …

Jun 29, 2015 · Since the factorial function is defined recursively, $(n+1)!=n! \cdot (n+1)$, your question boils down to whether or not the recurrence relation has a closed form solution, which …