Question

residue calculus / rational function = $\frac{P(z)}{Q(z)}$

score 146 · Answer 1 · 2023-02-05 16:43:08

146

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residue calculus / rational function = $\frac{P(z)}{Q(z)}$

Published on 05 Feb 2023 - 16:43

score 37 · Answer 2 · 2023-02-07 01:58:54

37

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Calculate $\int_{C} f(z)\ dz$ on the unit circle within a punctured disc.

Published on 07 Feb 2023 - 1:58

score 70 · Answer 3 · 2026-03-25 14:38:00

70

Views

Result of complex integral with branch cuts its imaginary, but shouldn't?

Published on 25 Mar 2026 - 14:38

score 292 · Answer 4 · 2026-02-23 10:20:07

292

Views

Pseudo Euler's identity (continuous) $ \int_{0}^{\infty} \frac{\pi^x}{\Gamma (x+1)} e^{\frac{i \pi x}{2}} dx =?$

Published on 23 Feb 2026 - 10:20

score 62 · Answer 5 · 2023-02-12 16:09:43

62

Views

$\int_0^{2\pi} \frac{rie^{it}}{re^{it}-a}dt$ without Cauchy integral theorem, residues, series.

Published on 12 Feb 2023 - 16:09

score 77 · Answer 6 · 2026-03-29 20:53:36

77

Views

How to calculate the integral $\frac{1}{2\pi i}\oint_{|z|=1}\frac{2(1-\cos(z))e^z}{z^4}dz$

Published on 29 Mar 2026 - 20:53

score 49 · Answer 7 · 2023-02-14 09:41:44

49

Views

Gaussian integral over complex interval

Published on 14 Feb 2023 - 9:41

score 58 · Answer 8 · 2023-02-16 03:38:01

58

Views

Is it possible to find the integral of ${\rm Re}(x)$ or ${\rm Im}(x)$?

Published on 16 Feb 2023 - 3:38

score 42 · Answer 9 · 2023-02-23 20:42:04

42

Views

Can the existence of antiderivative in complex plane implies the function is differentiable?

Published on 23 Feb 2023 - 20:42

score 108 · Answer 10 · 2023-02-27 02:34:45

108

Views

Evaluate $\int_{\gamma} \frac{1}{z^2 + z +1} \,dz$, where $\gamma$ is the circle $|z|=2$.

Published on 27 Feb 2023 - 2:34

score 87 · Answer 11 · 2026-03-27 08:38:43

87

Views

Complex integral on a simple closed curve

Published on 27 Mar 2026 - 8:38

score 119 · Answer 12 · 2023-03-01 15:32:15

119

Views

Prove that $|f^{'''}|\le 48$ for an analytic function $f$

Published on 01 Mar 2023 - 15:32

score 171 · Answer 13 · 2023-03-05 22:13:36

171

Views

My contour integrations seem to contradict the residue theorem.

Published on 05 Mar 2023 - 22:13

score 50 · Answer 14 · 2026-03-27 10:09:07

50

Views

Upper bound of a function in Hoffman and Mardsten's Complex Analysis 2.8

Published on 27 Mar 2026 - 10:09

score 145 · Answer 15 · 2026-04-01 07:17:08

145

Views

Finding the relation between Laplace and the CTFT

Published on 01 Apr 2026 - 7:17

List Question

residue calculus / rational function = $\frac{P(z)}{Q(z)}$

Calculate $\int_{C} f(z)\ dz$ on the unit circle within a punctured disc.

Result of complex integral with branch cuts its imaginary, but shouldn't?

Pseudo Euler's identity (continuous) $ \int_{0}^{\infty} \frac{\pi^x}{\Gamma (x+1)} e^{\frac{i \pi x}{2}} dx =?$

$\int_0^{2\pi} \frac{rie^{it}}{re^{it}-a}dt$ without Cauchy integral theorem, residues, series.

How to calculate the integral $\frac{1}{2\pi i}\oint_{|z|=1}\frac{2(1-\cos(z))e^z}{z^4}dz$

Gaussian integral over complex interval

Is it possible to find the integral of ${\rm Re}(x)$ or ${\rm Im}(x)$?

Can the existence of antiderivative in complex plane implies the function is differentiable?

Evaluate $\int_{\gamma} \frac{1}{z^2 + z +1} \,dz$, where $\gamma$ is the circle $|z|=2$.

Complex integral on a simple closed curve

Prove that $|f^{'''}|\le 48$ for an analytic function $f$

My contour integrations seem to contradict the residue theorem.

Upper bound of a function in Hoffman and Mardsten's Complex Analysis 2.8

Finding the relation between Laplace and the CTFT

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