List questions from residue-calculus

Published on 21 Feb 2020 - 14:02

304

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Find the analytic function $f(z)$

Published on 23 Feb 2020 - 15:32

45

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Prove that the solutions to the equation are purely imaginary

Published on 25 Feb 2020 - 10:06

63

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What is the residue of this function at $z=1$?

Published on 25 Feb 2020 - 12:26

292

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Calculate $\int_0^\infty\frac{x^a}{x^3+1} dx$ using residues

Published on 25 Feb 2020 - 13:06

166

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Find $f(z)$ given the modulus

Published on 26 Feb 2020 - 18:15

97

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Complex integration exercise with $\arctan $

Published on 29 Mar 2026 - 22:25

296

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Evaluating $\int_{0}^{2\pi} \frac{\mathrm{e}^{-i k a \cos\phi \sin\theta}}{1+\cos\phi \sin\theta}\,\mathrm d\phi$

Published on 29 Mar 2026 - 22:33

39

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Inconsistency in residue calculation?

Published on 05 Mar 2020 - 4:05

156

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Show that $\int_{0}^{\pi} \frac{1}{3+2\cos(t)}\mathrm{d}t = \frac{\pi}{\sqrt{5}}$

Published on 06 Mar 2020 - 10:34

71

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How to prove the Laurent series converges to the right thing?

Published on 26 Mar 2026 - 9:27

48

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What is the class of the singularity $5$ for $\exp(\frac{z}{z-5})$

Published on 26 Mar 2026 - 11:18

65

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Power series representation of $\frac{1}{1-e^z}$ to classify singularity.

Published on 26 Mar 2026 - 21:26

156

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When is the limit argument sufficient for showing poles?

Published on 26 Mar 2026 - 14:33

78

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Calculating residua of $f(z)=\frac{1}{z^3(1-z\operatorname{ctg}z)}$

Published on 08 Mar 2020 - 17:00

List Question

Imaginary part of $f(z)$

Find the analytic function $f(z)$

Prove that the solutions to the equation are purely imaginary

What is the residue of this function at $z=1$?

Calculate $\int_0^\infty\frac{x^a}{x^3+1} dx$ using residues

Find $f(z)$ given the modulus

Complex integration exercise with $\arctan $

Evaluating $\int_{0}^{2\pi} \frac{\mathrm{e}^{-i k a \cos\phi \sin\theta}}{1+\cos\phi \sin\theta}\,\mathrm d\phi$

Inconsistency in residue calculation?

Show that $\int_{0}^{\pi} \frac{1}{3+2\cos(t)}\mathrm{d}t = \frac{\pi}{\sqrt{5}}$

How to prove the Laurent series converges to the right thing?

What is the class of the singularity $5$ for $\exp(\frac{z}{z-5})$

Power series representation of $\frac{1}{1-e^z}$ to classify singularity.

When is the limit argument sufficient for showing poles?

Calculating residua of $f(z)=\frac{1}{z^3(1-z\operatorname{ctg}z)}$

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