Question

Compute $\int_{\gamma} \frac{1}{z-w}\mathrm dz, |w| \neq 1$ where $\gamma(t):=e^{it}, t \in [0, 2\pi]$

score 95 · Answer 1 · 2026-03-25 04:42:47

95

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Compute $\int_{\gamma} \frac{1}{z-w}\mathrm dz, |w| \neq 1$ where $\gamma(t):=e^{it}, t \in [0, 2\pi]$

Published on 25 Mar 2026 - 4:42

score 236 · Answer 2 · 2018-06-02 16:46:38

236

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Inequality used in computing Fresnel Integral

Published on 02 Jun 2018 - 16:46

score 124 · Answer 3 · 2026-03-25 03:07:01

124

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An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$

Published on 25 Mar 2026 - 3:07

score 743 · Answer 4 · 2018-06-09 18:56:28

743

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Solve $\int_{|z| = 3} \tan (\pi z) dz$ using argument principle

Published on 09 Jun 2018 - 18:56

score 267 · Answer 5 · 2026-03-25 11:28:50

267

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Proof that Integral over the arc vanishes as $R\rightarrow\infty$ in Inverse Mellin Transform of $\Gamma(s)$

Published on 25 Mar 2026 - 11:28

score 85 · Answer 6 · 2018-06-12 13:06:59

85

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How to find this singular integral?

Published on 12 Jun 2018 - 13:06

score 402 · Answer 7 · 2018-06-13 05:21:47

402

Views

Differentiation Under The Integral vs Contour Integration

Published on 13 Jun 2018 - 5:21

score 57 · Answer 8 · 2018-06-14 12:17:52

57

Views

Cauchy's formula - evaluating complex integrals

Published on 14 Jun 2018 - 12:17

score 53 · Answer 9 · 2026-03-26 21:09:29

53

Views

Show that $\int_{0}^{2\pi}\frac{1}{1+\alpha\cos^2(t)}dt=\frac{2\pi}{\sqrt{\lambda+1}}$ with $\alpha>-1$.

Published on 26 Mar 2026 - 21:09

score 66 · Answer 10 · 2018-06-15 01:34:09

66

Views

Can you use complex intervals for definite integrals?

Published on 15 Jun 2018 - 1:34

score 197 · Answer 11 · 2026-03-22 13:02:17

197

Views

Solving for a function inside a convolution

Published on 22 Mar 2026 - 13:02

score 189 · Answer 12 · 2026-03-25 21:48:50

189

Views

For $a>0$ compute $\int_0^\infty \frac{\log x}{(a + x)^3}\,dx$

Published on 25 Mar 2026 - 21:48

score 314 · Answer 13 · 2026-03-25 00:06:36

314

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Closed form solution of a contour integral involving Bessel function integral representation

Published on 25 Mar 2026 - 0:06

score 54 · Answer 14 · 2026-03-26 19:15:39

54

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Contour Integration of a simple expression

Published on 26 Mar 2026 - 19:15

score 163 · Answer 15 · 2026-03-28 05:23:22

163

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Problem: To show that $\int_{0}^{\infty}\sqrt[3]{(e^x-1)^2}\cdot \frac{dx}{1-2\cosh x}=-\frac{4}{3}\pi\sin\left(\frac{2}{9}\pi\right)$

Published on 28 Mar 2026 - 5:23

List Question

Compute $\int_{\gamma} \frac{1}{z-w}\mathrm dz, |w| \neq 1$ where $\gamma(t):=e^{it}, t \in [0, 2\pi]$

Inequality used in computing Fresnel Integral

An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$

Solve $\int_{|z| = 3} \tan (\pi z) dz$ using argument principle

Proof that Integral over the arc vanishes as $R\rightarrow\infty$ in Inverse Mellin Transform of $\Gamma(s)$

How to find this singular integral?

Differentiation Under The Integral vs Contour Integration

Cauchy's formula - evaluating complex integrals

Show that $\int_{0}^{2\pi}\frac{1}{1+\alpha\cos^2(t)}dt=\frac{2\pi}{\sqrt{\lambda+1}}$ with $\alpha>-1$.

Can you use complex intervals for definite integrals?

Solving for a function inside a convolution

For $a>0$ compute $\int_0^\infty \frac{\log x}{(a + x)^3}\,dx$

Closed form solution of a contour integral involving Bessel function integral representation

Contour Integration of a simple expression

Problem: To show that $\int_{0}^{\infty}\sqrt[3]{(e^x-1)^2}\cdot \frac{dx}{1-2\cosh x}=-\frac{4}{3}\pi\sin\left(\frac{2}{9}\pi\right)$

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