How do I find the factorial of a negative number?
Factorial as such is only defined for non-negative integers with the familiar recursive definition:
There are a couple of extensions of the definition of factorial to cover a larger domain.
Euler's gamma function
The most mainstream extension of the definition of factorial is given by Euler's gamma function,
For positive integers:
For any complex number
Then we can use the identity
This extends the definition of factorial to the negative integers as follows: