Factorial The Game

In recent times, factorial the game has become increasingly relevant in various contexts. What does the factorial of a negative number signify?. 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 need to arrange it? Something, which doesn't exist shouldn't have an arrangement right?

Can someone please throw some light on it?. factorial - Why does 0! - Mathematics Stack Exchange. It's important to note that, 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 we can cover those edge cases with the same formula, instead of having to treat them separately.

Additionally, we treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes ... complex analysis - Why is $i! = 0.498015668 - 0.154949828i .... This perspective suggests that, 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 give rise to any interesting geometric shapes/curves on the complex plane? Factorial, but with addition - Mathematics Stack Exchange. Factorial, but with addition [duplicate] Ask Question Asked 11 years, 11 months ago Modified 6 years, 3 months ago Defining the factorial of a real number - Mathematics Stack Exchange.

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. What is the practical application of factorials. 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 certain integrals, so mathematicians gave it a name and of course noted the relationship to factorials. See the graph at the end of this posting.

An easier method to calculate factorials? 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 following formula is obtained: Any shortcut to calculate factorial of a number (Without calculator or .... 12 I've been searching the internet for quite a while now to find anything useful that could help me to figure out how to calculate factorial of a certain number without using calculator but no luck whatsoever.