List questions from residue-calculus

Published on 25 Mar 2026 - 3:21

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square roots in multiplicative group of integers modulo n

Published on 25 Mar 2026 - 23:38

143

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Laurent series for $f(z) = \frac{\sinh(z + 3i)}{z(z + 3i)^3}$ at $-3i$ (not leaving as a product of series)

Published on 26 Mar 2026 - 0:56

363

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Complex integral $\oint_{|z|=1} \frac{z^2}{\sin^3 z \cos z} dz$

Published on 06 Jul 2018 - 23:59

125

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Complex integral with $\int_{+\partial D}\frac{\sin\left(\frac{1}{z}\right)\cos\left(\frac{1}{z-2}\right)}{z-5}\mathrm{dz}$

Published on 08 Jul 2018 - 13:17

82

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Finding the residue

Published on 11 Jul 2018 - 15:44

7.4k

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Find inverse Fourier transform of Lorentzian using complex integration

Published on 25 Mar 2026 - 23:37

120

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Computing a residue

Published on 13 Jul 2018 - 19:58

87

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For any positive integer $n \in \mathbb{N}, \text{Res} \Big ( \frac{1}{(1-e^{-z})^n} ;0 \Big ) = 1$.

Published on 15 Jul 2018 - 13:41

251

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Residue of $ctg(z)$

Published on 15 Jul 2018 - 14:09

56

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Residue of $\frac{1}{(z^2-1)^3}$ at the singularities.

Published on 15 Jul 2018 - 14:43

215

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Evaluate $\int_{|z|=3}\frac{dz}{z^3(z^{10}-2)}$

Published on 15 Jul 2018 - 16:19

1.1k

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Evaluate $\int_{|z|=4}\tan z dz$

Published on 16 Jul 2018 - 15:35

606

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Integrate $\int_{0}^{\infty} \frac{dx}{1 + x^n}$ using the Residue Theorem

Published on 17 Jul 2018 - 13:05

426

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Sum of Squares of Binomial Coefficients Using Residue Theorem

Published on 18 Jul 2018 - 4:26

List Question

Calculating Residue of $f^2$ with pole of order 2

square roots in multiplicative group of integers modulo n

Laurent series for $f(z) = \frac{\sinh(z + 3i)}{z(z + 3i)^3}$ at $-3i$ (not leaving as a product of series)

Complex integral $\oint_{|z|=1} \frac{z^2}{\sin^3 z \cos z} dz$

Complex integral with $\int_{+\partial D}\frac{\sin\left(\frac{1}{z}\right)\cos\left(\frac{1}{z-2}\right)}{z-5}\mathrm{dz}$

Finding the residue

Find inverse Fourier transform of Lorentzian using complex integration

Computing a residue

For any positive integer $n \in \mathbb{N}, \text{Res} \Big ( \frac{1}{(1-e^{-z})^n} ;0 \Big ) = 1$.

Residue of $ctg(z)$

Residue of $\frac{1}{(z^2-1)^3}$ at the singularities.

Evaluate $\int_{|z|=3}\frac{dz}{z^3(z^{10}-2)}$

Evaluate $\int_{|z|=4}\tan z dz$

Integrate $\int_{0}^{\infty} \frac{dx}{1 + x^n}$ using the Residue Theorem

Sum of Squares of Binomial Coefficients Using Residue Theorem

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