List questions from residue-calculus

Published on 26 Mar 2026 - 1:03

196

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Is $\int \frac{e^{z^2}}{z^3} dz=\pi i$? I got $2 \pi i$.

Published on 26 Mar 2026 - 1:03

108

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Prove $\frac{1}{2 \pi i}\int_{\gamma} \frac{gf'}{f} = \sum_{m=1}^{j} g(z_m) - \sum_{n=1}^{k} g(p_n)$.

Published on 25 Mar 2026 - 12:50

160

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Complex integral containing Gaussian

Published on 26 Mar 2026 - 1:06

161

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A Strange Mistake in Application of Residue theorem $\int_0^{2\pi}\frac {\cos(2\theta)} {5+4\cos(\theta)}\, d\theta.$

Published on 24 Jul 2018 - 13:30

394

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Find the residue of the function $f(z) = \frac{z^3}{(z-1)(z^4+2)}$ at $z=0$

Published on 24 Jul 2018 - 22:01

204

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Variation of residue theorem?

Published on 27 Jul 2018 - 13:35

64

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Residue on all layers of a complex function

Published on 27 Jul 2018 - 20:56

69

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What happens if I have an essential singularity and a pole for the same $z$?

Published on 25 Mar 2026 - 3:20

47

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Finding simple fraction decomposition with help of Taylor's Theorem and Residues theorem

Published on 31 Jul 2018 - 21:59

36

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Residue Calculus Integrable Model

Published on 31 Jul 2018 - 23:08

68

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Is $\int_{C[-2i,r]} \frac{dz}{z^2+1} = 0 , 1 < r < 3$? I got $-\pi$.

Published on 26 Mar 2026 - 1:04

794

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Residue at infinity calculating integrals

Published on 03 Aug 2018 - 21:59

211

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Calculating $\int_{-\infty}^{\infty}\left( \frac{\cos{\left (x \right )}}{x^{4} + 1} \right)dx$ via the Residue Theorem?

Published on 05 Aug 2018 - 23:24

596

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$f$ zero (essential singularity) $\implies \frac 1 f$ pole (essential singularity)

Published on 25 Mar 2026 - 3:18

List Question

Inverse Fourier transform of Lorentzians and sign function

Is $\int \frac{e^{z^2}}{z^3} dz=\pi i$? I got $2 \pi i$.

Prove $\frac{1}{2 \pi i}\int_{\gamma} \frac{gf'}{f} = \sum_{m=1}^{j} g(z_m) - \sum_{n=1}^{k} g(p_n)$.

Complex integral containing Gaussian

A Strange Mistake in Application of Residue theorem $\int_0^{2\pi}\frac {\cos(2\theta)} {5+4\cos(\theta)}\, d\theta.$

Find the residue of the function $f(z) = \frac{z^3}{(z-1)(z^4+2)}$ at $z=0$

Variation of residue theorem?

Residue on all layers of a complex function

What happens if I have an essential singularity and a pole for the same $z$?

Finding simple fraction decomposition with help of Taylor's Theorem and Residues theorem

Residue Calculus Integrable Model

Is $\int_{C[-2i,r]} \frac{dz}{z^2+1} = 0 , 1 < r < 3$? I got $-\pi$.

Residue at infinity calculating integrals

Calculating $\int_{-\infty}^{\infty}\left( \frac{\cos{\left (x \right )}}{x^{4} + 1} \right)dx$ via the Residue Theorem?

$f$ zero (essential singularity) $\implies \frac 1 f$ pole (essential singularity)

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