Question

Is $\int_{C[-2i,r]} \frac{dz}{z^2+1} = 0 , 1 < r < 3$? I got $-\pi$.

score 71 · Answer 1 · 2026-05-11 09:14:07

71

Views

Is $\int_{C[-2i,r]} \frac{dz}{z^2+1} = 0 , 1 < r < 3$? I got $-\pi$.

Published on 11 May 2026 - 9:14

score 192 · Answer 2 · 2026-05-10 17:38:17

192

Views

What closed paths make $\int_{\gamma} \frac 1 z dz = 2m \pi i$?

Published on 10 May 2026 - 17:38

score 708 · Answer 3 · 2026-04-16 22:03:08

708

Views

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Published on 16 Apr 2026 - 22:03

score 88 · Answer 4 · 2026-04-10 20:53:32

88

Views

Contour Integral of Geometric Series

Published on 10 Apr 2026 - 20:53

score 82 · Answer 5 · 2026-04-16 16:43:44

82

Views

Why dosen't the author consider $\oint_{\gamma_{R}} f(z) = 2 \pi i \sum_{j} Ind{\gamma}(P{j}) \cdot Res_{f}(P_{j})$?

Published on 16 Apr 2026 - 16:43

score 215 · Answer 6 · 2026-05-11 08:00:50

215

Views

Calculating $\int_{-\infty}^{\infty}\left( \frac{\cos{\left (x \right )}}{x^{4} + 1} \right)dx$ via the Residue Theorem?

Published on 11 May 2026 - 8:00

score 907 · Answer 7 · 2026-04-15 20:02:35

907

Views

Use contour integral to show $\int_0^{2\pi}\frac{\mathrm dt}{(1+\cos(u)\cos(t))^2}=\frac{2\pi}{\sin^3(u)}$ for $u\in(0,\frac{\pi}{2})$

Published on 15 Apr 2026 - 20:02

score 320 · Answer 8 · 2026-04-16 01:57:37

320

Views

Showing that $\int_{0}^{\infty} \frac{\cos(x)}{x^{2}+3}dx = \frac{e^{-\sqrt{3}} \pi}{2 \sqrt{3}}$ via Contour Integration?

Published on 16 Apr 2026 - 1:57

score 133 · Answer 9 · 2026-04-10 03:59:37

133

Views

Confusion regarding branch cut

Published on 10 Apr 2026 - 3:59

score 84 · Answer 10 · 2026-04-09 13:30:34

84

Views

Doubt in calculating $\sqrt {-i}$

Published on 09 Apr 2026 - 13:30

score 135 · Answer 11 · 2026-05-10 13:48:32

135

Views

Confusion with the Enneper-Weierstrass parametrization

Published on 10 May 2026 - 13:48

score 547 · Answer 12 · 2026-04-12 20:49:51

547

Views

A question about Jordan Lemma and estimation Lemma

Published on 12 Apr 2026 - 20:49

score 325 · Answer 13 · 2026-05-13 19:15:45

325

Views

Integration of digamma function

Published on 13 May 2026 - 19:15

score 229 · Answer 14 · 2026-04-11 20:37:25

229

Views

Calculate integral with $z^a$ using residue theorem

Published on 11 Apr 2026 - 20:37

score 44 · Answer 15 · 2026-04-16 11:17:13

44

Views

Contour integral by parts: convergent becomes divergent

Published on 16 Apr 2026 - 11:17

List Question

Is $\int_{C[-2i,r]} \frac{dz}{z^2+1} = 0 , 1 < r < 3$? I got $-\pi$.

What closed paths make $\int_{\gamma} \frac 1 z dz = 2m \pi i$?

Prove that $\int_0^\infty\,\frac{\sin(kx)}{x(x^2+1)}\,\text{d}x=\frac{\pi}{2}\,\left(1-\exp(-k)\right)$ for all $k\in\mathbb{R}_{\ge0}$.

Contour Integral of Geometric Series

Why dosen't the author consider $\oint_{\gamma_{R}} f(z) = 2 \pi i \sum_{j} Ind{\gamma}(P{j}) \cdot Res_{f}(P_{j})$?

Calculating $\int_{-\infty}^{\infty}\left( \frac{\cos{\left (x \right )}}{x^{4} + 1} \right)dx$ via the Residue Theorem?

Use contour integral to show $\int_0^{2\pi}\frac{\mathrm dt}{(1+\cos(u)\cos(t))^2}=\frac{2\pi}{\sin^3(u)}$ for $u\in(0,\frac{\pi}{2})$

Showing that $\int_{0}^{\infty} \frac{\cos(x)}{x^{2}+3}dx = \frac{e^{-\sqrt{3}} \pi}{2 \sqrt{3}}$ via Contour Integration?

Confusion regarding branch cut

Doubt in calculating $\sqrt {-i}$

Confusion with the Enneper-Weierstrass parametrization

A question about Jordan Lemma and estimation Lemma

Integration of digamma function

Calculate integral with $z^a$ using residue theorem

Contour integral by parts: convergent becomes divergent

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