List questions from branch-cuts

Published on 07 Jun 2020 - 12:30

162

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Let $a\in\mathbb{C}, |a|=1$ and $c$ an irrational real number. Prove: $a^c$ is dense in the unit circle.

Published on 28 Jun 2020 - 14:39

51

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Inverse Fourier involving branch cut

Published on 04 Jul 2020 - 20:48

67

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If $f(0) = 0$, $f$ injective, then there is single-valued branch of $\sqrt{f(z^2)}$

Published on 06 Jul 2020 - 0:18

1.3k

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Branch cut of square root

Published on 25 Jul 2020 - 17:56

34

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Finding domain where this complex logarithm identity holds

Published on 22 Jul 2016 - 2:42

378

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Contour integral of $\sqrt[3]{z^3-1}$ on $|z| = 2$ and branches

Published on 25 Mar 2026 - 3:21

325

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Definite Integral with Branch Points

Published on 25 Mar 2026 - 3:17

206

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Fourier Type Integral with Branch Cut

Published on 14 Aug 2016 - 11:27

193

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Integral Along Positive Real Axis in the Presence of a Branch Cut: $\int_0^\infty dt \frac{\exp(-t/\alpha)}{(p - bt)^q}$

Published on 22 Mar 2026 - 18:00

172

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Choosing the correct branch in $\int \frac{a-\cos(\theta)}{b-\cos(\theta)} d\theta$

Published on 02 Sep 2016 - 16:10

514

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Branch Points of the function $z^{(1 + i)}$

Published on 25 Mar 2026 - 3:23

1.3k

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branch points and cuts for log

Published on 25 Mar 2026 - 3:18

12.2k

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Branch cuts for $\sqrt{z^2+1}$

Published on 25 Mar 2026 - 3:22

6k

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Trick of finding branch points

Published on 25 Mar 2026 - 3:19

List Question

How to evaluate this contour integral with branches?

Let $a\in\mathbb{C}, |a|=1$ and $c$ an irrational real number. Prove: $a^c$ is dense in the unit circle.

Inverse Fourier involving branch cut

If $f(0) = 0$, $f$ injective, then there is single-valued branch of $\sqrt{f(z^2)}$

Branch cut of square root

Finding domain where this complex logarithm identity holds

Contour integral of $\sqrt[3]{z^3-1}$ on $|z| = 2$ and branches

Definite Integral with Branch Points

Fourier Type Integral with Branch Cut

Integral Along Positive Real Axis in the Presence of a Branch Cut: $\int_0^\infty dt \frac{\exp(-t/\alpha)}{(p - bt)^q}$

Choosing the correct branch in $\int \frac{a-\cos(\theta)}{b-\cos(\theta)} d\theta$

Branch Points of the function $z^{(1 + i)}$

branch points and cuts for log

Branch cuts for $\sqrt{z^2+1}$

Trick of finding branch points

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