Question

Compute $\int_{-\infty}^{\infty} \frac{x^{2}}{(1+x^{4})^{2}} dx$ using residues

score 184 · Answer 1 · 2019-12-11 21:15:33

184

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Compute $\int_{-\infty}^{\infty} \frac{x^{2}}{(1+x^{4})^{2}} dx$ using residues

Published on 11 Dec 2019 - 21:15

score 307 · Answer 2 · 2019-12-12 07:40:11

307

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Gamma-Distribution-like integral

Published on 12 Dec 2019 - 7:40

score 44 · Answer 3 · 2019-12-12 18:58:56

44

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What is $\int_c {e^{z^2}}(1/{z^2} - 1/{z^3})$ when c is the unit circle?

Published on 12 Dec 2019 - 18:58

score 165 · Answer 4 · 2019-12-17 15:41:15

165

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How to integrate $\int_{C} \frac{z^2}{(z^4 +1)}$ where $C$ is $|z + i| = 1$

Published on 17 Dec 2019 - 15:41

score 128 · Answer 5 · 2026-02-23 00:47:56

128

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A Third Derivative in Ahlfors' `Some Remarks on Teichmuller Space'

Published on 23 Feb 2026 - 0:47

score 126 · Answer 6 · 2019-12-21 18:13:53

$P(z)=a_0+a_1z+a_2z^2+...+a_nz^n , a_k\in\mathbb{R}$ a complex polynomial prove: $a_k= \frac{1}{2\pi i}\oint_{|z|=1}z^{k-1}\overline{P(z)}dz$.

score 169 · Answer 7 · 2026-03-25 19:04:40

169

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How to calculate principal value of this complex integral?

Published on 25 Mar 2026 - 19:04

score 118 · Answer 8 · 2026-03-28 05:59:59

118

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Finding residues in a complex integral $\int_0^\infty\frac{z^6\,\mathrm{d}z}{(z^4+1)^2}$ using Laurent series expansion

Published on 28 Mar 2026 - 5:59

score 41 · Answer 9 · 2019-12-23 14:05:21

41

Views

Evaluating a class of complex integrals

Published on 23 Dec 2019 - 14:05

score 135 · Answer 10 · 2019-12-27 16:17:22

135

Views

How to prove $ \iint_{\mathbb D}\frac{1}{\left|1-\bar{z}\zeta\right|^4}\mathrm dx\mathrm dy = \frac{\pi}{(1-|\zeta|^2)^2} $?

Published on 27 Dec 2019 - 16:17

score 210 · Answer 11 · 2026-03-26 07:37:34

210

Views

Using complex integral methods evaluate this real integral

Published on 26 Mar 2026 - 7:37

score 360 · Answer 12 · 2026-03-26 09:39:57

360

Views

Fourier Transform of a $N$-dimensional complex Gaussian

Published on 26 Mar 2026 - 9:39

score 33 · Answer 13 · 2019-12-29 02:55:23

33

Views

Double integral (averaging) of an error function in a complex plane in an area such as circle

Published on 29 Dec 2019 - 2:55

score 96 · Answer 14 · 2020-01-02 19:19:55

96

Views

Calculate a complex integral

Published on 02 Jan 2020 - 19:19

score 150 · Answer 15 · 2026-03-26 17:31:42

150

Views

Sum of roots with residue theorem

Published on 26 Mar 2026 - 17:31

List Question

Compute $\int_{-\infty}^{\infty} \frac{x^{2}}{(1+x^{4})^{2}} dx$ using residues

Gamma-Distribution-like integral

What is $\int_c {e^{z^2}}(1/{z^2} - 1/{z^3})$ when c is the unit circle?

How to integrate $\int_{C} \frac{z^2}{(z^4 +1)}$ where $C$ is $|z + i| = 1$

A Third Derivative in Ahlfors' `Some Remarks on Teichmuller Space'

$P(z)=a_0+a_1z+a_2z^2+...+a_nz^n , a_k\in\mathbb{R}$ a complex polynomial prove: $a_k= \frac{1}{2\pi i}\oint_{|z|=1}z^{k-1}\overline{P(z)}dz$.

How to calculate principal value of this complex integral?

Finding residues in a complex integral $\int_0^\infty\frac{z^6\,\mathrm{d}z}{(z^4+1)^2}$ using Laurent series expansion

Evaluating a class of complex integrals

How to prove $ \iint_{\mathbb D}\frac{1}{\left|1-\bar{z}\zeta\right|^4}\mathrm dx\mathrm dy = \frac{\pi}{(1-|\zeta|^2)^2} $?

Using complex integral methods evaluate this real integral

Fourier Transform of a $N$-dimensional complex Gaussian

Double integral (averaging) of an error function in a complex plane in an area such as circle

Calculate a complex integral

Sum of roots with residue theorem

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