Factorial of $i$

Question

With $i^2=-1$, what is $i!$ ?

I'm not sure if it is $i$ or if it is an infinite product $i(i-1)(i-2)(i-3)(i-4)(i-5)\dots$

It would make sense either way.

Is it not defined?

Answer 1

Check out http://en.wikipedia.org/wiki/Gamma_function

$$\Gamma(i+1) \approx 0.498015668 - 0.154949828\, i $$