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Wikipedia error about the complementary error function?

  1. Aug 2, 2012 #1
    Take a trip over here and explain to me what is meant by taking the double factorial of [itex]-1[/itex]. If you try to let [itex]N = 1[/itex] in the remainder formula, you wind up having to take [itex](2(0) - 1)!! = (-1)!![/itex], right? This strikes me as a typo; should it be changed? If so, to what?
     
  2. jcsd
  3. Aug 2, 2012 #2

    marcusl

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    They clearly intend that (-1)!!=1.
     
  4. Aug 2, 2012 #3

    Mute

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

    [tex](2k-1)!! = \frac{(2k)!}{2^k k!}.[/tex]

    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.
     
  5. Aug 3, 2012 #4
    So I'm guessing that if I set [itex]N = 1[/itex], then what we have is

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

    Can anyone confirm this?
     
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