Factorial of a negative number

[spectrum123]

Main Question or Discussion Point

Is it possible to find the factorial of a negative real number ? If possible, then what is its practical application ?

 

[jedishrfu]

here's some discussion on the matter:

http://mathoverflow.net/questions/10124/the-factorial-of-1-2-3

and

http://mathforum.org/library/drmath/view/60851.html

 

[D H]

What about positive real numbers? Not just 1, 2, 3, ..., but also 1.5, pi, etc.

The generalization of the factorial is the gamma function. For various reasons there's an offset of one: $\Gamma(n) = (n-1)!$. The gamma function is defined for complex numbers as well as real numbers. The only exception are non-positive real integers. The gamma function "blows up" at 0, -1, -2, etc.