# Can n! ever be negative?

1. ### gikiian

98
If yes, then for what values of n?

2. ### R136a1

341
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

1 person likes this.
3. ### lurflurf

2,325
If we extend the domain we can have negative numbers for example
-1~(-3.74768264672741260139148848269149969586163939513235551205229915)!
-1~(-3.45702473822080062303945414765117954323659790903378442096479450)!

4. ### gikiian

98
THAT is what I wanted to see. Thank you very much Sir.

Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted