Question

Proof that $\int_0^\infty\frac{\ln x}{x^3 - 1} \, dx = \frac{4 \pi^2}{27}$

score 688 · Answer 1 · 2020-12-06 21:34:28

688

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Proof that $\int_0^\infty\frac{\ln x}{x^3 - 1} \, dx = \frac{4 \pi^2}{27}$

Published on 06 Dec 2020 - 21:34

score 121 · Answer 2 · 2026-03-25 20:39:39

121

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Singularity structure of a multivalued function

Published on 25 Mar 2026 - 20:39

score 155 · Answer 3 · 2020-12-24 12:40:01

155

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How can I calculate $\log(e^{e^i})$?

Published on 24 Dec 2020 - 12:40

score 99 · Answer 4 · 2026-02-23 04:19:05

99

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Lipschitz constant estimation of continuous selection of upper hemicontinuous multivalued function

Published on 23 Feb 2026 - 4:19

score 36 · Answer 5 · 2021-04-12 07:09:38

36

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How to find the modulus of a complex components?

Published on 12 Apr 2021 - 7:09

score 164 · Answer 6 · 2021-04-29 13:20:36

164

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Putnam Problem A3 2010: if $h=a\frac{\partial h}{\partial x}+b\frac{\partial h}{\partial y}$ and $h$ is bounded then $h\equiv0$

Published on 29 Apr 2021 - 13:20

score 32 · Answer 7 · 2021-04-29 13:57:14

32

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The definition of surjective multivalued

Published on 29 Apr 2021 - 13:57

score 77 · Answer 8 · 2021-05-06 19:06:44

77

Views

Find the joint distribution and covariance with exponential density

Published on 06 May 2021 - 19:06

score 105 · Answer 9 · 2021-05-27 21:26:41

105

Views

Let $f(z)$ be a complex function whose value is $\sqrt{z^2-1}\in\Bbb R$ when $z\in \Bbb R$ and $z>1$, and $f(z)$ is holomorphic if $1<|z|<\infty$

Published on 27 May 2021 - 21:26

score 280 · Answer 10 · 2021-06-02 16:32:59

280

Views

Compare the limits of $(Z^2-1)^{\frac{1}{2}}$ above and below its branch cut.

Published on 02 Jun 2021 - 16:32

score 286 · Answer 11 · 2021-06-16 09:38:25

286

Views

Definition of directional derivative: Why does it work?

Published on 16 Jun 2021 - 9:38

score 289 · Answer 12 · 2021-06-21 10:47:19

289

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How to find principal branch of a complex multivalued function?

Published on 21 Jun 2021 - 10:47

score 82 · Answer 13 · 2021-08-12 07:15:02

82

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Relation of solutions of differential equations around different singular points

Published on 12 Aug 2021 - 7:15

score 136 · Answer 14 · 2021-08-16 19:16:30

136

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Solving $C\cos(\sqrt\lambda\theta)+D\sin(\sqrt\lambda\theta)=C\cos(\sqrt\lambda(\theta+2m\pi)) + D\sin(\sqrt\lambda (\theta + 2m\pi))$

Published on 16 Aug 2021 - 19:16

score 288 · Answer 15 · 2021-09-15 06:26:15

288

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What is the inverse in the complex plane of $e^z + z$?

Published on 15 Sep 2021 - 6:26

List Question

Proof that $\int_0^\infty\frac{\ln x}{x^3 - 1} \, dx = \frac{4 \pi^2}{27}$

Singularity structure of a multivalued function

How can I calculate $\log(e^{e^i})$?

Lipschitz constant estimation of continuous selection of upper hemicontinuous multivalued function

How to find the modulus of a complex components?

Putnam Problem A3 2010: if $h=a\frac{\partial h}{\partial x}+b\frac{\partial h}{\partial y}$ and $h$ is bounded then $h\equiv0$

The definition of surjective multivalued

Find the joint distribution and covariance with exponential density

Let $f(z)$ be a complex function whose value is $\sqrt{z^2-1}\in\Bbb R$ when $z\in \Bbb R$ and $z>1$, and $f(z)$ is holomorphic if $1<|z|<\infty$

Compare the limits of $(Z^2-1)^{\frac{1}{2}}$ above and below its branch cut.

Definition of directional derivative: Why does it work?

How to find principal branch of a complex multivalued function?

Relation of solutions of differential equations around different singular points

Solving $C\cos(\sqrt\lambda\theta)+D\sin(\sqrt\lambda\theta)=C\cos(\sqrt\lambda(\theta+2m\pi)) + D\sin(\sqrt\lambda (\theta + 2m\pi))$

What is the inverse in the complex plane of $e^z + z$?

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