# Tagged Questions

For questions about integration methods that use results from complex analysis and their applications

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### Evaluating the complex integral- Correct approach?

I'm asked to evaluate the following complex integral with C being the unit circle: $$\oint_{C}^{}{\log(z-z_0)dz}\quad |z_0|>1$$ $\log(z-z_0)$ is multivalued and has a branch point at $z=z_0$. ...
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In many textbooks, the following fermionic Matsubara sum is given as a useful identity: $$T\sum_{\omega_n}\frac{1}{i\omega_n-\epsilon}=\frac{1}{e^{\epsilon/T}+1},$$ where $\omega_n=n\pi T$ for all odd ...
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### Infinite total variation of complex measure in Feynman path integral

I am trying to understand this: If one tries to define a Feynman path integral as a Wiener integral, then the complex measure could be of infinite total variation. What exactly does this mean? How ...
I'm trying to integrate with a closed contour on the upper-half of the complex plane. $I = \displaystyle\int_{-\infty}^\infty \dfrac{z\,\mathrm{sech(z)}}{[(z-a)^2+b^2][(z+a)^2+b^2]} dz$ There are ...