Factorial of Negative Numbers!

Hello friends, today I'm going to talk about factorial of Negative Numbers.

In mathematics, factorial of a positive Integer say n is given as 

where '*' is multiplication sign.

you know 0! is taken as 1.

Factorial of a positive integers have great applications in Programming and mathematics. Permutations and combinations is one (where we find the number of ways a group of objects can be arranged or selected in given group of objects). Expansion of terms like (a+b)^n (binomial theorem) are computed using factorials.

We'll discuss about how to find factorials of very large numbers like say 100! or 1000! in programming in my upcoming posts.

Well, let's discuss about factorials about negative numbers here...
 
This is the one way to 0!, put n=0, and we get 0!=1

See the above formula, there is a problem with the factorial of Negative Number, did you get it? No?? ok, if you want to find factorial of -1 then 
put n =-1 and see,

 
which is not defined!

If we go on this way. for every number 'n' , (-n)! =  not defined.

therefore, factorial of negative number is not possible.

But what if we define it some other way?

Why can't we take factorial of negative number as -

OR


Idea is to deal with factorial differently when using for a positive number as compared to a negative number. Different identities and different formulas for negative numbers and positive numbers will exist.

Hope this helps!

Further read...

Extension of Factorials Concept

Page on Mathoverflow