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, and we …

May 7, 2012 · One common math puzzle I've seen around asks for how many zeros are in the product of "100!" Usually, the solution everyone gives goes something like try to match pairs of 5s and 2s that …

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 we e...

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 …

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 …

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 …

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)

Jul 16, 2020 · Explore related questions polynomials factorial binomial-theorem See similar questions with these tags.

Dec 20, 2014 · How many digits are there in 100 factorial? How does one calculate the number of digits?