Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Gold Member

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


    User Avatar
    Homework Helper

    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

    \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?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Wikipedia error about the complementary error function?
  1. Error Function (Replies: 7)

  2. Error function (Replies: 1)