Factorials of Negative Integers

Date: 06/27/2002 at 02:21:04
From: Steven
Subject: factorial

Is it possible to compute the factorial of a negative number, e.g., 

  (-4)! = ?

Date: 06/28/2002 at 05:33:31
From: Doctor Floor
Subject: Re: factorial

Hi, Steven,

Thanks for your question.

Starting from the explanation for 0! in the Dr. Math FAQ,

  0! = 1
  http://mathforum.org/dr.math/faq/faq.0factorial.html 

if we try to extend this to -1, we find that (-1)! = 1/0 which means
that (-1!) is undefined. Extending further to (-2)! etc. is thus
impossible as well.

The same FAQ mentions the Gamma function, which generalizes the idea
of factorial to non-integer numbers.  Note that this function also
yields undefined values for negative integer factorials. 

If you have more questions, just write back.

Best regards,

- Doctor Floor, The Math Forum
  http://mathforum.org/dr.math/