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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.

betel

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# Problems with identity in complex calc

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