Dopefish wrote:I don't think n! is defined for anything except non-negative integers.
The gamma function is the extension to factorial, that works for whatever you want to feed it. Given the stuff above didn't at all look like a non-negative integer (or even real), it strictly speaking probably should have been a gamma function involved.
I really hate to get bogged down in semantics, but I disagree.
The factorial is defined for all complex numbers except for negative integers. That's why when I punch 9.5! into my calculator it returns a number, not "undefined". For numbers apart from non-negative integers, It happens to be defined in terms of the gamma function, but that doesn't make it not valid.
It's the same way that the sine function is defined in terms of the exponential function or that the gamma function itself is defined in terms of an integral.