# Wikipedia error about the complementary error function?

1. Aug 2, 2012

### 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?

2. Aug 2, 2012

### marcusl

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

3. Aug 2, 2012

### 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.

4. Aug 3, 2012

### AxiomOfChoice

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

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

Can anyone confirm this?