# How do I find the factorial of a negative number?

##### 1 Answer

It depends.

#### Explanation:

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

**Roman factorial**

This extends the definition of factorial to the negative integers as follows: