Question

Applying Cauchy's Integral Formula for $\oint_{|z|=4} \frac{e^{1 /(z-1)}}{z-2} d z$

score 171 · Answer 1 · 2026-03-29 12:28:21

171

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Applying Cauchy's Integral Formula for $\oint_{|z|=4} \frac{e^{1 /(z-1)}}{z-2} d z$

Published on 29 Mar 2026 - 12:28

score 53 · Answer 2 · 2020-12-05 22:53:27

53

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Solving complex improper integrals

Published on 05 Dec 2020 - 22:53

score 193 · Answer 3 · 2020-12-06 16:51:24

193

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Interesting real integrals from $ I=\oint\limits_{C}\sin(\frac{1}{z})\,\mathrm{dz} = 2\pi i $

Published on 06 Dec 2020 - 16:51

score 725 · Answer 4 · 2026-03-25 19:04:39

725

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Cauchy's residue theorem extended to branch cuts

Published on 25 Mar 2026 - 19:04

score 113 · Answer 5 · 2026-03-29 12:23:57

113

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Complex integral over two differents closed path

Published on 29 Mar 2026 - 12:23

score 124 · Answer 6 · 2020-12-11 08:58:11

124

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Simple zero $a$ is equal to $\frac{1}{2\pi i}\int_C \frac{zf'(a)}{f(z)} dz$ for $f$ holomorphic within $C$?

Published on 11 Dec 2020 - 8:58

score 64 · Answer 7 · 2026-03-29 12:23:57

64

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Integral Contour

Published on 29 Mar 2026 - 12:23

score 65 · Answer 8 · 2026-04-07 19:28:23

65

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Studying for qualifying exams. Complex analysis identity

Published on 07 Apr 2026 - 19:28

score 93 · Answer 9 · 2020-12-14 13:10:44

93

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How to understand the residue $\text{Res}(\frac{e^{iz}}{\sinh(z)},0) = \frac{e^{iz}}{\cosh(z)}\bigg|_{z=0}$

Published on 14 Dec 2020 - 13:10

score 305 · Answer 10 · 2020-12-14 13:51:55

305

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Using Argument principle to find roots of complex polynomial. Studying for qualifying exam

Published on 14 Dec 2020 - 13:51

score 175 · Answer 11 · 2026-03-27 16:25:20

175

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Show that : $\int_{0}^{\infty}\arctan\left(\frac{2}{x^2+1}\right)dx=\pi\sqrt{\phi^{-1}}$

Published on 27 Mar 2026 - 16:25

score 58 · Answer 12 · 2020-12-16 16:06:38

58

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Estimating the integral

Published on 16 Dec 2020 - 16:06

score 67 · Answer 13 · 2026-02-23 15:33:30

67

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Integrating $\int_0^\infty \frac{\ln t}{t^2+a^2}\,dt$ with residue theorem.

Published on 23 Feb 2026 - 15:33

score 466 · Answer 14 · 2020-12-17 22:03:21

466

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Integral $\int_0^\infty \frac{\ln(x)}{1-x^2} \; dx$ using residue theorem

Published on 17 Dec 2020 - 22:03

score 76 · Answer 15 · 2026-03-29 12:28:20

76

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Complex Integration Question : Integrate $f(z) = x^2+iy^2$ when $z(t) = t^2+it^2$ and $0 \le t \le 1$

Published on 29 Mar 2026 - 12:28

List Question

Applying Cauchy's Integral Formula for $\oint_{|z|=4} \frac{e^{1 /(z-1)}}{z-2} d z$

Solving complex improper integrals

Interesting real integrals from $ I=\oint\limits_{C}\sin(\frac{1}{z})\,\mathrm{dz} = 2\pi i $

Cauchy's residue theorem extended to branch cuts

Complex integral over two differents closed path

Simple zero $a$ is equal to $\frac{1}{2\pi i}\int_C \frac{zf'(a)}{f(z)} dz$ for $f$ holomorphic within $C$?

Integral Contour

Studying for qualifying exams. Complex analysis identity

How to understand the residue $\text{Res}(\frac{e^{iz}}{\sinh(z)},0) = \frac{e^{iz}}{\cosh(z)}\bigg|_{z=0}$

Using Argument principle to find roots of complex polynomial. Studying for qualifying exam

Show that : $\int_{0}^{\infty}\arctan\left(\frac{2}{x^2+1}\right)dx=\pi\sqrt{\phi^{-1}}$

Estimating the integral

Integrating $\int_0^\infty \frac{\ln t}{t^2+a^2}\,dt$ with residue theorem.

Integral $\int_0^\infty \frac{\ln(x)}{1-x^2} \; dx$ using residue theorem

Complex Integration Question : Integrate $f(z) = x^2+iy^2$ when $z(t) = t^2+it^2$ and $0 \le t \le 1$

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