Sep 10, 2020 · As I studied, I found factorials for positive reals and negative fractions. But the integral with which we define factorial falls flat on the negative integers. why is that we can find …

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 …

Jan 13, 2015 · (A riff on a deleted answer:) Any polynomial sequence has a rational generating function of the form $\frac {P (x)} { (1-x)^k}$. This can be seen by repeatedly differentiating the …

Jun 21, 2015 · The sub-factorial is actually defined combinatorially, and that value is what turns up. It is the number of symmetries on $\ {1,\dots,n\}$ with no fixed points.

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, …

5 This question already has answers here: The product of $n$ consecutive integers is divisible by $n$ factorial (7 answers)

Jun 1, 2018 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …

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 …

Plugging in numbers shows me that it is the same, but I don't know how to get from one to the other. I get stuck at: $$ n!(n+1) = n n! + n! $$ I can't make the connection for the final step. $(...

You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …