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 …

Apr 21, 2015 · Closed 12 years ago. 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 to …

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 …

Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)? Here is an example: 5!...

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, the …

Moreover, they start getting the factorial of negative numbers, like $-\frac {1} {2}! = \sqrt {\pi}$ How is this possible? What is the definition of the factorial of a fraction? What about negative numbers? I tried …

Apr 7, 2015 · Which rule is applied to define the operator precedence for factorial Ask Question Asked 10 years, 8 months ago Modified 7 years, 9 months ago

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 …

Below is the etymology, from Jeff Miller's Earliest Known Uses of Some of the Words of Mathematics (F). Perhaps a native French speaker can lend further insight. FACTORIAL. The earlier term faculty …

Dec 27, 2019 · The expression mentioned in your question is a reflection of the fact that there are actually two "nice" extensions of the double factorial (one agreeing with it on even numbers and the …