Wikipedia error about the complementary error function?

[AxiomOfChoice]

Take a trip over here and explain to me what is meant by taking the double factorial of -1. If you try to let N = 1 in the remainder formula, you wind up having to take (2(0) - 1)! = (-1)!, right? This strikes me as a typo; should it be changed? If so, to what?

 

[marcusl]

They clearly intend that (-1)!=1.

 

[Mute]

If you look at the page for double factorial, they note that for odd integers it can be expressed as

(2k-1)! = \frac{(2k)!}{2^k k!}.

Setting k = 0 gives (-1)! = 1. The original formula is derived for k > 0, but one can take the formula to work for k = 0 by convention, I guess.

 

[AxiomOfChoice]

So I'm guessing that if I set N = 1, then what we have is

<br /> \text{erfc}(x) = \frac{e^{-x^2}}{x \sqrt \pi} + O \left(x e^{-x^2} \right) \quad \text{as $x\to \infty$}.<br />

Can anyone confirm this?