List questions from branch-cuts

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edge disjoin Cut Set

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possible results of integral along closed path after defining branch of sqrt

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Choose the branch for $(1-\zeta^2)^{1/2}$ that makes it holomorphic in the upper half-plane and positive when $-1<\zeta<1$

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power series expansion of $z^a$ at $z = 1$

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Contour integral with branch point

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List Question

handwaving substitution in integral involving branch cut and derivative of sqrt + generalization

edge disjoin Cut Set

possible results of integral along closed path after defining branch of sqrt

Finding branch points and branch cuts of arctan

Analytical Continuation

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Complex exponent properties?

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How many values does $1^{\alpha}$ have for $\alpha$ irrational?

Choose the branch for $(1-\zeta^2)^{1/2}$ that makes it holomorphic in the upper half-plane and positive when $-1<\zeta<1$

power series expansion of $z^a$ at $z = 1$

Defining a branch of $(1-\zeta^2)^{-1/2}$

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