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Complex integration: pole of order 2 at zero

score 223 · Answer 1 · 2026-03-26 08:14:11

223

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Complex integration: pole of order 2 at zero

Published on 26 Mar 2026 - 8:14

score 170 · Answer 2 · 2020-12-03 07:06:33

170

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

Published on 03 Dec 2020 - 7:06

score 559 · Answer 3 · 2020-12-04 00:06:16

559

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Compute the integral of $f=\frac{1}{z^2}$ along the given contour $T$.

Published on 04 Dec 2020 - 0:06

score 1.2k · Answer 4 · 2020-12-04 12:20:11

1.2k

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$\int \frac{(e^z)}{z-\pi i} dz$, if C is the ellipse |z - 2| + |z+2| = 6

Published on 04 Dec 2020 - 12:20

score 51 · Answer 5 · 2020-12-04 13:33:37

$ \frac {1}{2\pi i} \int \frac {(e^z)}{z-\pi i} dz$, around a rectangle with vertices at: $(a)$ $2 \pm i$,$ -2 \pm i$ $(b)$ $-i, 2 - i, 2 + i, i.$

score 112 · Answer 6 · 2020-12-10 16:03:13

112

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Complex integral over two differents closed path

Published on 10 Dec 2020 - 16:03

score 46 · Answer 7 · 2020-12-11 03:23:04

46

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Does Cauchy rule apply if singularity is on the contour?

Published on 11 Dec 2020 - 3:23

score 63 · Answer 8 · 2020-12-13 05:22:46

63

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Integral Contour

Published on 13 Dec 2020 - 5:22

score 75 · Answer 9 · 2020-12-17 22:05:36

75

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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 17 Dec 2020 - 22:05

score 118 · Answer 10 · 2020-12-19 14:55:04

118

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Show that if $f$ is analytic on $B(z_0,r)\setminus\{z_0\}$, and $ \lim_{z\to z_0} f(z)(z-z_0)=A$ , then, $\oint_{|z-z_0|=r} f(z) dz=2\pi iA$

Published on 19 Dec 2020 - 14:55

score 60 · Answer 11 · 2020-12-21 06:27:54

60

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Using Cauchy Integral Formula to Solve $\int_\gamma (z-(4+4i))\sin(\frac{1}{z+(3-3i)})dz$

Published on 21 Dec 2020 - 6:27

score 389 · Answer 12 · 2020-12-23 13:48:05

389

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For which $p$, does there exist an anti-derivative?

Published on 23 Dec 2020 - 13:48

score 64 · Answer 13 · 2020-12-25 12:26:28

64

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Complex analysis. Cauchy's integral formula

Published on 25 Dec 2020 - 12:26

score 140 · Answer 14 · 2020-12-25 13:16:52

140

Views

Why is the independence of paths for complex integrals not sufficient enough to proof Cauchy's integral theorem?

Published on 25 Dec 2020 - 13:16

score 68 · Answer 15 · 2026-03-26 06:34:18

68

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A proof about Boundary Asymptotics of the Cauchy Transform using the Dominated Convergence Theorem

Published on 26 Mar 2026 - 6:34

List Question

Complex integration: pole of order 2 at zero

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

Compute the integral of $f=\frac{1}{z^2}$ along the given contour $T$.

$\int \frac{(e^z)}{z-\pi i} dz$, if C is the ellipse |z - 2| + |z+2| = 6

$ \frac {1}{2\pi i} \int \frac {(e^z)}{z-\pi i} dz$, around a rectangle with vertices at: $(a)$ $2 \pm i$,$ -2 \pm i$ $(b)$ $-i, 2 - i, 2 + i, i.$

Complex integral over two differents closed path

Does Cauchy rule apply if singularity is on the contour?

Integral Contour

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

Show that if $f$ is analytic on $B(z_0,r)\setminus\{z_0\}$, and $ \lim_{z\to z_0} f(z)(z-z_0)=A$ , then, $\oint_{|z-z_0|=r} f(z) dz=2\pi iA$

Using Cauchy Integral Formula to Solve $\int_\gamma (z-(4+4i))\sin(\frac{1}{z+(3-3i)})dz$

For which $p$, does there exist an anti-derivative?

Complex analysis. Cauchy's integral formula

Why is the independence of paths for complex integrals not sufficient enough to proof Cauchy's integral theorem?

A proof about Boundary Asymptotics of the Cauchy Transform using the Dominated Convergence Theorem

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