Last non Zero digit of a Factorial Ask Question Asked 14 years ago Modified 2 years 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 need to arrange it? Something, which doesn't exist shouldn't have an arrangement right? Can someone please throw some light on it?.
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 give rise to any interesting geometric shapes/curves on the complex plane?
4 $$ \frac {n!} {e^n} = \prod_ {i=1}^n\frac {i} {e}. $$ Since $$ \lim_ {i \to \infty} \frac {i} {e} = \infty, $$ clearly the factorial is growing faster than the exponential.
limits - Does this prove that the factorial grows faster than the ...
One definition of the factorial that is more general than the usual $$ N! = N\cdot (N-1) \dots 1 $$ is via the gamma function, where $$ \Gamma (N) = (N-1)! = \int_0^ {\infty} x^ {N-1}e^ {-x} dx $$ This definition is not limited to positive integers, and in fact can be taken as the definition of the factorial for non-integers. With this definition, you can quite clearly see that $$ 0! = \Gamma ...
Why is 0 factorial equal to 1? Is there any pure basic mathematical ...
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 is not defined. $\Gamma (x)$ is related to the factorial in that it is equal to $ (x-1)!$.