Question

$\int_{\Gamma}\frac{e^{z}dz}{z(z^{2}-1)}$ as $\Gamma$ is rectangle contour that does not passes through the points $0,1,-1$

score 50 · Answer 1 · 2022-11-05 14:50:22

50

Views

$\int_{\Gamma}\frac{e^{z}dz}{z(z^{2}-1)}$ as $\Gamma$ is rectangle contour that does not passes through the points $0,1,-1$

Published on 05 Nov 2022 - 14:50

score 63 · Answer 2 · 2026-04-09 05:30:39

63

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Doubt about evaluating an integral

Published on 09 Apr 2026 - 5:30

score 45 · Answer 3 · 2026-04-11 07:41:33

45

Views

Get residues of the function inside a closed contour

Published on 11 Apr 2026 - 7:41

score 43 · Answer 4 · 2026-04-08 17:40:57

43

Views

Functional equation in quaternion algebra

Published on 08 Apr 2026 - 17:40

score 70 · Answer 5 · 2022-11-08 15:18:44

70

Views

Evaluate $\int_{\gamma} \frac{2 \sin(z) +e^z}{z^2 - 2z} dz$ where $\gamma = C(0,3)$ with positive orientation.

Published on 08 Nov 2022 - 15:18

score 38 · Answer 6 · 2022-11-08 16:58:31

Evaluate: $\int_{\gamma} \frac{e^{\cos z}}{(z^2 + 1)^2} dz$, where $\gamma$ is a set of made of positive and negative orientation circles.

score 78 · Answer 7 · 2022-11-08 23:58:19

$\gamma: \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \to \mathbb C$, $\gamma (t) = 2e^{it}$. Calculate: $\int_{\gamma} \frac{z}{z^2 + 1} dz$.

score 38 · Answer 8 · 2026-04-11 18:53:06

38

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Inequality of Complex Integral

Published on 11 Apr 2026 - 18:53

score 131 · Answer 9 · 2022-11-10 10:46:35

131

Views

calculate the integral $\int_{-\infty}^{\infty} \frac{dx}{(x^2 + 1)^3}$ by using the residue theorem

Published on 10 Nov 2022 - 10:46

score 289 · Answer 10 · 2026-04-09 15:21:06

289

Views

Show that the two elliptic integrals are equal

Published on 09 Apr 2026 - 15:21

score 100 · Answer 11 · 2022-11-12 09:17:55

100

Views

Contour integral of $z\mapsto \frac{1}{z(z-1)}$ over the positively oriented circle with radius $\frac12$

Published on 12 Nov 2022 - 9:17

score 53 · Answer 12 · 2022-11-12 14:58:42

53

Views

Branch cuts for inverse hyperbolic function

Published on 12 Nov 2022 - 14:58

score 44 · Answer 13 · 2026-04-12 04:28:33

44

Views

A conceptual question on complex plane: Can we do any other type of integration on a complex plane?

Published on 12 Apr 2026 - 4:28

score 49 · Answer 14 · 2026-04-08 21:27:07

49

Views

Using Cauchy integral formula with real constants powers

Published on 08 Apr 2026 - 21:27

score 50 · Answer 15 · 2022-11-14 14:39:39

50

Views

Calculate $\int_{-\infty}^{\infty} \frac{\sin (ax)}{x^2 + x +1}dx$

Published on 14 Nov 2022 - 14:39

List Question

$\int_{\Gamma}\frac{e^{z}dz}{z(z^{2}-1)}$ as $\Gamma$ is rectangle contour that does not passes through the points $0,1,-1$

Doubt about evaluating an integral

Get residues of the function inside a closed contour

Functional equation in quaternion algebra

Evaluate $\int_{\gamma} \frac{2 \sin(z) +e^z}{z^2 - 2z} dz$ where $\gamma = C(0,3)$ with positive orientation.

Evaluate: $\int_{\gamma} \frac{e^{\cos z}}{(z^2 + 1)^2} dz$, where $\gamma$ is a set of made of positive and negative orientation circles.

$\gamma: \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] \to \mathbb C$, $\gamma (t) = 2e^{it}$. Calculate: $\int_{\gamma} \frac{z}{z^2 + 1} dz$.

Inequality of Complex Integral

calculate the integral $\int_{-\infty}^{\infty} \frac{dx}{(x^2 + 1)^3}$ by using the residue theorem

Show that the two elliptic integrals are equal

Contour integral of $z\mapsto \frac{1}{z(z-1)}$ over the positively oriented circle with radius $\frac12$

Branch cuts for inverse hyperbolic function

A conceptual question on complex plane: Can we do any other type of integration on a complex plane?

Using Cauchy integral formula with real constants powers

Calculate $\int_{-\infty}^{\infty} \frac{\sin (ax)}{x^2 + x +1}dx$

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