(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose a complex integral of the form

[tex] \int_{-\infty}^{\infty}(\frac {1}{\alpha+i\lambda}-\frac{1}{\beta +i \lambda}) log(-i\mu\lambda) d\lambda [/tex]

where

[tex]\alpha,\beta[/tex]

are arbitrary positive parameters and the sufficient condition for integrability (nonlatttice, etc) is assumed. The branch cut lies on the negative real axis i.e. [tex]C1; [-r,-R]U[re^{i\theta}:-\pi<θ<0]U[r,R]U[Re^{iθ}i<θ<0] [/tex]

2. Relevant equations

3. The attempt at a solution

Haven't learned how to get its residue first of all. Second of all the integrand is multiplied by log(-iμλ} which I haven't dealt with before.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Log(-i mu lambda)

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