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Problems with identity in complex calc

  1. Jan 18, 2010 #1

    in a paper I have the identity

    [tex] \int_{-\infty}^{\infty} d x \sqrt{(x-i\epsilon)^2-1}= I_+ - I_- + i \int_{-1}^{1}(\ldots) [/tex]

    where [tex]I_+ = \int_1^{\infty}(\ldots), I_=\int_{-\infty}^{-1}(\ldots)[/tex] and [tex] \epsilon[/tex] is a small positive number that will be taken to zero at the end.

    My Problem is to get the minus sign between [tex]I_+[/tex] and [tex]I_-[/tex]. In all my calculations I get +. The integrand for both should be [tex]\sqrt{x^2-1}[/tex].

    Can anybody tell me what I am missing here to get the correct sign.
    Thanks in advance.
  2. jcsd
  3. Jan 18, 2010 #2


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    Science Advisor

    I think it's essential what you (or the author) means by "(...)" for the integrand.
  4. Jan 18, 2010 #3
    In further calculations the author uses [tex] \sqrt{x^2-1}[/tex]. The integrand is definitely real.
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