- #1
betel
- 318
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Hello,
in a paper I have the identity
\int_{-\infty}^{\infty} d x \sqrt{(x-i\epsilon)^2-1}= I_+ - I_- + i \int_{-1}^{1}(\ldots)
where I_+ = \int_1^{\infty}(\ldots), I_=\int_{-\infty}^{-1}(\ldots) and \epsilon is a small positive number that will be taken to zero at the end.
My Problem is to get the minus sign between I_+ and I_-. In all my calculations I get +. The integrand for both should be \sqrt{x^2-1}.
Can anybody tell me what I am missing here to get the correct sign.
Thanks in advance.
betel
in a paper I have the identity
\int_{-\infty}^{\infty} d x \sqrt{(x-i\epsilon)^2-1}= I_+ - I_- + i \int_{-1}^{1}(\ldots)
where I_+ = \int_1^{\infty}(\ldots), I_=\int_{-\infty}^{-1}(\ldots) and \epsilon is a small positive number that will be taken to zero at the end.
My Problem is to get the minus sign between I_+ and I_-. In all my calculations I get +. The integrand for both should be \sqrt{x^2-1}.
Can anybody tell me what I am missing here to get the correct sign.
Thanks in advance.
betel
