List questions from residue-calculus

Published on 10 May 2026 - 11:20

100

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Complex integral $I=\int_{|z|=2} \frac{z^3 e^{\frac{1}{z}}}{z+1}dz$

Published on 17 Apr 2026 - 13:37

411

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PV of $\int_{-\infty}^\infty \frac{x^n~ e^{-ax^2} dx}{(x-x_1)(x-x_2)},~ (n=0,1,2,3,...)$

Published on 10 May 2026 - 12:34

3.8k

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Intuitive reason why contour integral around origin of $z^n$ is 0 unless n = -1

Published on 14 Apr 2026 - 2:27

1k

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Inverse Mellin Transform of gamma function products

Published on 30 Apr 2026 - 13:33

295

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Complex analysis: Improper integral of a non-even function

Published on 10 May 2026 - 13:46

568

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Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$

Published on 16 Apr 2026 - 7:30

121

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Regulating divergent integrals in the complex plane

Published on 13 Apr 2026 - 12:04

144

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Evaluating Trig Integrals with Residues

Published on 12 Apr 2026 - 7:55

46

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Is there any complex integral that is singular and cannot be solved using residue theorems?

Published on 11 Apr 2026 - 7:31

186

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Complex analysis: Using the residue at infinity to show $\int_Cp(z)/q(z)dz = 0$

Published on 13 Apr 2026 - 2:37

86

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Finding the Laurent series of the following function

Published on 13 Apr 2026 - 19:20

95

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Evaluating real integrals through residues

Published on 12 Apr 2026 - 2:48

118

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Calculate residue in every pole of $\frac{z^2}{(z-2)^2(\cos{z}-1)^3}$

Published on 16 Apr 2026 - 4:37

256

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Use residues to solve this real integral:$\int_0^{2\pi}\arctan\left[\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)+3}\right]\,d\theta$

Published on 18 Apr 2026 - 11:47

List Question

An approach to evaluating a Cauchy principal value that yields unexpected extra imaginary term

Complex integral $I=\int_{|z|=2} \frac{z^3 e^{\frac{1}{z}}}{z+1}dz$

PV of $\int_{-\infty}^\infty \frac{x^n~ e^{-ax^2} dx}{(x-x_1)(x-x_2)},~ (n=0,1,2,3,...)$

Intuitive reason why contour integral around origin of $z^n$ is 0 unless n = -1

Inverse Mellin Transform of gamma function products

Complex analysis: Improper integral of a non-even function

Arc contribution in $\int_{-\infty}^\infty \mathrm{d}z \frac{e^{-z^2}}{z-1}$

Regulating divergent integrals in the complex plane

Evaluating Trig Integrals with Residues

Is there any complex integral that is singular and cannot be solved using residue theorems?

Complex analysis: Using the residue at infinity to show $\int_Cp(z)/q(z)dz = 0$

Finding the Laurent series of the following function

Evaluating real integrals through residues

Calculate residue in every pole of $\frac{z^2}{(z-2)^2(\cos{z}-1)^3}$

Use residues to solve this real integral:$\int_0^{2\pi}\arctan\left[\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)+3}\right]\,d\theta$

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