Question

Principal value integral by contour integration

score 312 · Answer 1 · 2021-06-06 19:20:43

312

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Principal value integral by contour integration

Published on 06 Jun 2021 - 19:20

score 391 · Answer 2 · 2026-03-26 11:16:47

391

Views

Sokhotski–Plemelj theorem for two-dimensional integrals

Published on 26 Mar 2026 - 11:16

score 29 · Answer 3 · 2021-06-10 04:44:45

29

Views

Finding residue to show reverse Fourier Transform

Published on 10 Jun 2021 - 4:44

score 327 · Answer 4 · 2021-06-11 08:28:35

327

Views

Determine a unique square root for a holomorphic function on a simply connected set

Published on 11 Jun 2021 - 8:28

score 283 · Answer 5 · 2021-06-11 08:55:04

283

Views

Complex integration to solve real integral $\int_{0}^{2}\frac{\sqrt{x\left(2-x\right)}}{\left(x+1\right)^{2}\left(3-x\right)}dx.$

Published on 11 Jun 2021 - 8:55

score 182 · Answer 6 · 2021-06-11 16:46:15

182

Views

Fourier Transform of $\frac{1}{2\pi} \int\limits_{0}^{2\pi}e^{ir\sin\theta}e^{2i\theta} d\theta$?

Published on 11 Jun 2021 - 16:46

score 60 · Answer 7 · 2021-06-12 18:47:41

60

Views

Holomorphic Parameterintegral

Published on 12 Jun 2021 - 18:47

score 96 · Answer 8 · 2021-06-12 20:44:07

96

Views

Complex integration $\int_{0}^{1}\frac{\sqrt[3]{4x^{2}\left(1-x\right)}}{\left(1+x\right)^{3}}dx$

Published on 12 Jun 2021 - 20:44

score 108 · Answer 9 · 2021-06-13 20:08:20

108

Views

If $\displaystyle \int_\gamma f(z) \, dz = i$ and $\displaystyle\int_\gamma g(z)\,dz = 3-i,$ find $\displaystyle\int_{-\gamma} (2f(z) + ig(z))\,dz$?

Published on 13 Jun 2021 - 20:08

score 193 · Answer 10 · 2021-06-14 19:01:37

193

Views

A uniform bound on a family of complex integrals

Published on 14 Jun 2021 - 19:01

score 91 · Answer 11 · 2021-06-16 10:50:22

91

Views

Compute $\int_0^\infty \frac{x}{(1+x)^6}dx$ using residue

Published on 16 Jun 2021 - 10:50

score 33 · Answer 12 · 2026-03-26 17:52:48

33

Views

How to know a complex function is analytic without going to the whole process of checking Cauchy-Riemann condition?

Published on 26 Mar 2026 - 17:52

score 70 · Answer 13 · 2021-06-17 13:02:24

70

Views

$u$ substitution leads to invalid result

Published on 17 Jun 2021 - 13:02

score 52 · Answer 14 · 2026-03-29 20:21:44

52

Views

Show $\frac{2}{\pi} \int_{0}^{2\pi} f(e^{i\theta})\cos^2(\frac{\theta}{2})d\theta = 2f(0)+f'(0)$ when $f\in A(|z|<1+\varepsilon)$.

Published on 29 Mar 2026 - 20:21

score 100 · Answer 15 · 2026-03-29 20:20:50

100

Views

I'm stuck in complex integration on Cauchy integral theorem example is in image and recommended books.

Published on 29 Mar 2026 - 20:20

List Question

Principal value integral by contour integration

Sokhotski–Plemelj theorem for two-dimensional integrals

Finding residue to show reverse Fourier Transform

Determine a unique square root for a holomorphic function on a simply connected set

Complex integration to solve real integral $\int_{0}^{2}\frac{\sqrt{x\left(2-x\right)}}{\left(x+1\right)^{2}\left(3-x\right)}dx.$

Fourier Transform of $\frac{1}{2\pi} \int\limits_{0}^{2\pi}e^{ir\sin\theta}e^{2i\theta} d\theta$?

Holomorphic Parameterintegral

Complex integration $\int_{0}^{1}\frac{\sqrt[3]{4x^{2}\left(1-x\right)}}{\left(1+x\right)^{3}}dx$

If $\displaystyle \int_\gamma f(z) \, dz = i$ and $\displaystyle\int_\gamma g(z)\,dz = 3-i,$ find $\displaystyle\int_{-\gamma} (2f(z) + ig(z))\,dz$?

A uniform bound on a family of complex integrals

Compute $\int_0^\infty \frac{x}{(1+x)^6}dx$ using residue

How to know a complex function is analytic without going to the whole process of checking Cauchy-Riemann condition?

$u$ substitution leads to invalid result

Show $\frac{2}{\pi} \int_{0}^{2\pi} f(e^{i\theta})\cos^2(\frac{\theta}{2})d\theta = 2f(0)+f'(0)$ when $f\in A(|z|<1+\varepsilon)$.

I'm stuck in complex integration on Cauchy integral theorem example is in image and recommended books.

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