List questions from branch-cuts

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Evaluate the integral $\int_{\gamma} \frac{dz}{z+\frac{1}{2}-\frac{i}{3}}$

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There is no branch of $\arg z$ in $\{0 \lt |z| \lt 1 \}$ using the fact that $\int_{\gamma} \frac{dz}{z}=2\pi i$

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Help with the integral $\int_{0}^{\infty}\log\left(1+\frac{s^{2}}{4\pi^{2}} \log(1+ix)\right ) e^{-2\pi nx}dx$

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Calculate integrals concerning a branch

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Integration imaginary and real part with branch cut

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What is the domain of the function f(z) = log(z) if it has a branch cut at angle alpha in rectangular coordinates?

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compute the complex-valued integral for the branch cut

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Regarding branch cuts and contour integration: $ \int_0^1 \frac{dx}{\sqrt{x^2-1}} $

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Contour integration with a branch cut. Parameterizing f(z) properly

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List Question

Inverting complex cosine

How to define Square Root

Complex Analysis Branch cuts

Evaluate the integral $\int_{\gamma} \frac{dz}{z+\frac{1}{2}-\frac{i}{3}}$

There is no branch of $\arg z$ in $\{0 \lt |z| \lt 1 \}$ using the fact that $\int_{\gamma} \frac{dz}{z}=2\pi i$

Help with the integral $\int_{0}^{\infty}\log\left(1+\frac{s^{2}}{4\pi^{2}} \log(1+ix)\right ) e^{-2\pi nx}dx$

Calculate integrals concerning a branch

Integration imaginary and real part with branch cut

What is a branch cut?

What is a simple way of describing branch cuts?

Integration: Branch cuts

What is the domain of the function f(z) = log(z) if it has a branch cut at angle alpha in rectangular coordinates?

compute the complex-valued integral for the branch cut

Regarding branch cuts and contour integration: $ \int_0^1 \frac{dx}{\sqrt{x^2-1}} $

Contour integration with a branch cut. Parameterizing f(z) properly

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