# Can n! ever be negative?

1. Dec 1, 2013

### gikiian

If yes, then for what values of n?

2. Dec 1, 2013

### R136a1

We usually only define $n!$ for natural numbers $n$. Then $n!$ can never be negative.

There is however a very natural extension of the factorial, this is called the Pi function (which is just a translation of the Gamma function). This can indeed become negative as you can see from the graph: http://en.wikipedia.org/wiki/Gamma_function

3. Dec 1, 2013

### lurflurf

If we extend the domain we can have negative numbers for example
-1~(-3.74768264672741260139148848269149969586163939513235551205229915)!
-1~(-3.45702473822080062303945414765117954323659790903378442096479450)!

4. Dec 1, 2013

### gikiian

THAT is what I wanted to see. Thank you very much Sir.