Factorial Of A Number Means

In recent times, factorial of a number means has become increasingly relevant in various contexts. complex analysis - Why is $i! = 0.498015668 - 0.154949828i .... 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? In this context, do complex factorials give rise to any interesting geometric shapes/curves on the complex plane? Equally important, factorial, but with addition - Mathematics Stack Exchange. Another key aspect involves, factorial, but with addition [duplicate] Ask Question Asked 11 years, 11 months ago Modified 6 years, 3 months ago

What does the factorial of a negative number signify?. Furthermore, 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? In relation to this, can someone please throw some light on it?. 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. Furthermore, factorial - Why does 0!

In this context, - Mathematics Stack Exchange. The theorem that $\binom {n} {k} = \frac {n!} {k! Similarly, (n-k)!}$ already assumes $0!$ is defined to be $1$. Otherwise this would be restricted to $0 <k < n$.

From another angle, 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. We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes ... Derivative of a factorial - Mathematics Stack Exchange. 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. How do we calculate factorials for numbers with decimal places?. 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? Another key aspect involves, like $2!$ is $2\\times1$, but how do we e...

Any shortcut to calculate factorial of a number (Without calculator or ....