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Using residues to evaluate a sum involving the square of $\text{csch}$

score 1.8k · Answer 1 · 2026-04-13 00:32:26

1.8k

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Using residues to evaluate a sum involving the square of $\text{csch}$

Published on 13 Apr 2026 - 0:32

score 96 · Answer 2 · 2026-04-14 19:16:12

96

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calculate $\oint_{|z|=1}z^{2018}e^{\frac{1}{z}}\sin\frac{1}{z}\text{dz}$

Published on 14 Apr 2026 - 19:16

score 1.7k · Answer 3 · 2026-04-16 13:11:41

1.7k

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calculate: $\int_{0}^{2\pi}e^{\cos\theta}(\cos(n\theta-\sin\theta))d\theta$

Published on 16 Apr 2026 - 13:11

score 318 · Answer 4 · 2026-04-16 06:10:32

318

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calculate: $\int_0^\infty \frac{\log x \, dx}{(x+a)(x+b)}$ using contour integration

Published on 16 Apr 2026 - 6:10

score 106 · Answer 5 · 2026-04-11 19:42:29

106

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Computing contour integral of $\frac{|z-a|^2}{z|z-b|^2}$ on unit circle and understanding it

Published on 11 Apr 2026 - 19:42

score 236 · Answer 6 · 2026-04-14 17:06:54

236

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Calculate: $\int_{0}^{\infty}\frac{\sin x}{x^{3}+x}\mathrm{d}x$ ;find my mistake

Published on 14 Apr 2026 - 17:06

score 221 · Answer 7 · 2026-04-16 02:40:33

221

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Calculate $\int_0^\infty \frac{\ln x}{\sqrt{x}(x+1)} \, \mathrm{d}x$

Published on 16 Apr 2026 - 2:40

score 239 · Answer 8 · 2026-04-17 02:33:45

239

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Calculate :$\int_{0}^{2\pi }e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$

Published on 17 Apr 2026 - 2:33

score 127 · Answer 9 · 2026-04-13 23:19:23

127

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calculate $\oint_{|z|=1} \left(\frac{z}{z-a}\right)^n \, dz$

Published on 13 Apr 2026 - 23:19

score 1.5k · Answer 10 · 2026-04-16 11:54:28

1.5k

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Prove $ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$.

Published on 16 Apr 2026 - 11:54

score 66 · Answer 11 · 2026-04-23 00:16:03

66

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Inverse Fourier transform in two dimensions

Published on 23 Apr 2026 - 0:16

score 249 · Answer 12 · 2026-04-16 10:51:14

249

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Calculate:$\int_{0}^{\infty}\frac{\ln x}{(x+1)^{3}}\mathrm{d}x$ with contour integration

Published on 16 Apr 2026 - 10:51

score 457 · Answer 13 · 2026-04-10 18:46:27

457

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On Complex Improper Integrals and Rectifiable Paths

Published on 10 Apr 2026 - 18:46

score 371 · Answer 14 · 2026-04-16 00:36:18

371

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calculate: $\int_{-\infty}^{\infty}\frac{\cos\frac{\pi}{2}x}{1-x^{2}}dx$ using complex analysis ; detect my mistake

Published on 16 Apr 2026 - 0:36

score 47 · Answer 15 · 2026-04-16 03:51:57

47

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What is the correct way to do $\int_{-1}^1 \frac {dx}{x+1+2i} $?

Published on 16 Apr 2026 - 3:51

List Question

Using residues to evaluate a sum involving the square of $\text{csch}$

calculate $\oint_{|z|=1}z^{2018}e^{\frac{1}{z}}\sin\frac{1}{z}\text{dz}$

calculate: $\int_{0}^{2\pi}e^{\cos\theta}(\cos(n\theta-\sin\theta))d\theta$

calculate: $\int_0^\infty \frac{\log x \, dx}{(x+a)(x+b)}$ using contour integration

Computing contour integral of $\frac{|z-a|^2}{z|z-b|^2}$ on unit circle and understanding it

Calculate: $\int_{0}^{\infty}\frac{\sin x}{x^{3}+x}\mathrm{d}x$ ;find my mistake

Calculate $\int_0^\infty \frac{\ln x}{\sqrt{x}(x+1)} \, \mathrm{d}x$

Calculate :$\int_{0}^{2\pi }e^{R{ {\cos t}}}\cos(R\sin t+3t)\mathrm{d}t$

calculate $\oint_{|z|=1} \left(\frac{z}{z-a}\right)^n \, dz$

Prove $ \int_0^\infty e^{-x^2} dx = \frac{\sqrt{\pi}}{2}$.

Inverse Fourier transform in two dimensions

Calculate:$\int_{0}^{\infty}\frac{\ln x}{(x+1)^{3}}\mathrm{d}x$ with contour integration

On Complex Improper Integrals and Rectifiable Paths

calculate: $\int_{-\infty}^{\infty}\frac{\cos\frac{\pi}{2}x}{1-x^{2}}dx$ using complex analysis ; detect my mistake

What is the correct way to do $\int_{-1}^1 \frac {dx}{x+1+2i} $?

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