Question

How to evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{1+\cos^2\theta}\,d\theta$ using residues?

score 486 · Answer 1 · 2026-03-29 17:27:36

486

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How to evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{1+\cos^2\theta}\,d\theta$ using residues?

Published on 29 Mar 2026 - 17:27

score 79 · Answer 2 · 2026-03-29 17:27:09

79

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Using the Residue Theorem evaluate $\int_{C}{e^\frac{1}{z}dz}$

Published on 29 Mar 2026 - 17:27

score 209 · Answer 3 · 2026-03-29 17:31:48

209

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Fourier transform through residues with real singularity

Published on 29 Mar 2026 - 17:31

score 64 · Answer 4 · 2020-01-12 17:58:55

64

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Show that $\sum_{n=-\infty}^{\infty} \operatorname{Res}[f(z), n] = 2 \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1)^{3}}$

Published on 12 Jan 2020 - 17:58

score 312 · Answer 5 · 2020-01-13 18:47:13

312

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Evaluate the integral p.v. $\int_{-\infty}^\infty\frac{\mathrm{e}^{-2\mathrm{i}x}}{x^2+1}\,\mathrm{d}x$ using residues

Published on 13 Jan 2020 - 18:47

score 189 · Answer 6 · 2026-03-29 19:17:36

189

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Evaluate the integral $\int_{C}\frac{z^{3}e^{\frac{1}{z}}}{1+z^{3}}dz$.

Published on 29 Mar 2026 - 19:17

score 34 · Answer 7 · 2020-01-17 17:25:53

34

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Residue for $\int_{-\infty}^{\infty} \frac{1}{\left(x^{2}+1\right)^{3}} d x$ problem with second derivative.

Published on 17 Jan 2020 - 17:25

score 111 · Answer 8 · 2020-01-18 16:59:18

111

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Looking for a curve for calculating this integral using Residue Theorem

Published on 18 Jan 2020 - 16:59

score 235 · Answer 9 · 2026-03-26 08:00:40

235

Views

What's the residue of $xe^{\frac{1}{x}}$ in $x=0$?

Published on 26 Mar 2026 - 8:00

score 166 · Answer 10 · 2020-01-25 00:39:25

166

Views

Methods for evaluating $\sum_{n=1}^\infty \frac1{a+(n-1)n}$

Published on 25 Jan 2020 - 0:39

score 110 · Answer 11 · 2020-01-25 01:52:24

110

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What is the integral of $\exp(iz)$?

Published on 25 Jan 2020 - 1:52

score 142 · Answer 12 · 2026-03-29 19:15:56

142

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Calculating integral $\int_{-\infty}^{\infty}\frac{1}{(1+y^2)^2}dy$ using Residue theorem

Published on 29 Mar 2026 - 19:15

score 68 · Answer 13 · 2020-01-28 06:34:54

68

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Evaluating definite integrals via contours

Published on 28 Jan 2020 - 6:34

score 50 · Answer 14 · 2020-01-28 09:45:46

50

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Compute a Integral Probably Applying Residue

Published on 28 Jan 2020 - 9:45

score 179 · Answer 15 · 2020-01-29 16:55:39

179

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Value of $I$ where $I=\frac{1}{2\pi i} \oint_{\gamma}z^7\cos(\frac{1}{z^2})dz$

Published on 29 Jan 2020 - 16:55

List Question

How to evaluate $\int_0^{2\pi} \frac{\sin^2\theta}{1+\cos^2\theta}\,d\theta$ using residues?

Using the Residue Theorem evaluate $\int_{C}{e^\frac{1}{z}dz}$

Fourier transform through residues with real singularity

Show that $\sum_{n=-\infty}^{\infty} \operatorname{Res}[f(z), n] = 2 \sum_{n=0}^{\infty} \frac{(-1)^{n}}{(2 n+1)^{3}}$

Evaluate the integral p.v. $\int_{-\infty}^\infty\frac{\mathrm{e}^{-2\mathrm{i}x}}{x^2+1}\,\mathrm{d}x$ using residues

Evaluate the integral $\int_{C}\frac{z^{3}e^{\frac{1}{z}}}{1+z^{3}}dz$.

Residue for $\int_{-\infty}^{\infty} \frac{1}{\left(x^{2}+1\right)^{3}} d x$ problem with second derivative.

Looking for a curve for calculating this integral using Residue Theorem

What's the residue of $xe^{\frac{1}{x}}$ in $x=0$?

Methods for evaluating $\sum_{n=1}^\infty \frac1{a+(n-1)n}$

What is the integral of $\exp(iz)$?

Calculating integral $\int_{-\infty}^{\infty}\frac{1}{(1+y^2)^2}dy$ using Residue theorem

Evaluating definite integrals via contours

Compute a Integral Probably Applying Residue

Value of $I$ where $I=\frac{1}{2\pi i} \oint_{\gamma}z^7\cos(\frac{1}{z^2})dz$

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