On Tue, 16 Jun 2020 at 09:55, Bruce Momjian <bruce@momjian.us> wrote:
>
> On Tue, Jun 16, 2020 at 08:31:21AM +0100, Dean Rasheed wrote:
> >
> > Most common implementations do regard factorial as undefined for
> > anything other than positive integers, as well as following the
> > convention that factorial(0) = 1. Some implementations extend the
> > factorial to non-integer inputs, negative inputs, or even complex
> > inputs by defining it in terms of the gamma function. However, even
> > then, it is undefined for negative integer inputs.
>
> Wow, they define it for negative inputs, but not negative integer
> inputs? I am curious what the logic is behind that.
>
That's just the way the maths works out. The gamma function is
well-defined for all real and complex numbers except for zero and
negative integers, where it has poles (singularities/infinities).
Actually the gamma function isn't the only possible extension of the
factorial function, but it's the one nearly everyone uses, if they
bother at all (most people don't).
Curiously, the most widespread implementation is probably the
calculator in MS Windows.
Regards,
Dean