List questions from contour-integration

Published on 09 Apr 2026 - 22:56

117

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Breakdown of Inverse Transform from Contour Integral at short times

Published on 24 Apr 2026 - 3:51

79

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On evaluating $\rho(s)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma(z)P(sz)\,dz.$

Published on 16 Apr 2026 - 10:31

247

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Integrate $\frac{\log(x^2+4)}{(x^2+1)^2}$.

Published on 17 Apr 2026 - 1:59

116

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Computing $\int_{-\infty}^{+\infty} e^{-iky} e^{-c|k|^{\alpha}} |k|^{\beta} dk$

Published on 25 Apr 2026 - 10:05

122

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Cauchy principal value for an integral with poles on path of integration

Published on 26 Mar 2026 - 21:25

208

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Why is $\int_0^\infty \frac{2 \cos(x) + x^2 - 2}{x^4}dx = \frac{\pi}{6}$?

Published on 16 Apr 2026 - 9:25

989

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Cauchy's integral formula when $z_0$ lies outside of contour w/o residue thrm

Published on 12 Apr 2026 - 11:05

62

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Evaluating integral using residue

Published on 10 Apr 2026 - 18:12

960

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Contour Integral to show $\int_{-\infty}^\infty \frac{e^{-2\pi i x\xi}}{(1 + x^2)^2}\,\mathrm{d}x = \frac{\pi}{2}(1+2\pi|\xi|)e^{-2\pi|\xi|}$.

Published on 14 Apr 2026 - 20:23

188

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Evaluate $\int_{-\infty}^{\infty}\frac{1-\cos(x)}{x^2}e^{ikx}dx$

Published on 17 Apr 2026 - 16:04

140

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For a bounded operator $A$, show that $(fg)(A)=f(A)g(A)$

Published on 14 Apr 2026 - 0:38

109

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Calculate $\int_{-\infty}^{\infty}\frac{\cos^2(x)}{x^2}e^{-ikx}dx$ for $k\in[0,2]$

Published on 16 Apr 2026 - 13:11

178

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Contour integral of $\displaystyle\oint_{c} \frac{e^{ix}}{1+z^{2}} dz$

Published on 13 Apr 2026 - 20:25

64

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Complex integral of $\lvert z-i\rvert$ along a line

Published on 10 Apr 2026 - 11:19

List Question

How to obtain the equality between two integrals with different integrands?

Breakdown of Inverse Transform from Contour Integral at short times

On evaluating $\rho(s)=\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\Gamma(z)P(sz)\,dz.$

Integrate $\frac{\log(x^2+4)}{(x^2+1)^2}$.

Computing $\int_{-\infty}^{+\infty} e^{-iky} e^{-c|k|^{\alpha}} |k|^{\beta} dk$

Cauchy principal value for an integral with poles on path of integration

Why is $\int_0^\infty \frac{2 \cos(x) + x^2 - 2}{x^4}dx = \frac{\pi}{6}$?

Cauchy's integral formula when $z_0$ lies outside of contour w/o residue thrm

Evaluating integral using residue

Contour Integral to show $\int_{-\infty}^\infty \frac{e^{-2\pi i x\xi}}{(1 + x^2)^2}\,\mathrm{d}x = \frac{\pi}{2}(1+2\pi|\xi|)e^{-2\pi|\xi|}$.

Evaluate $\int_{-\infty}^{\infty}\frac{1-\cos(x)}{x^2}e^{ikx}dx$

For a bounded operator $A$, show that $(fg)(A)=f(A)g(A)$

Calculate $\int_{-\infty}^{\infty}\frac{\cos^2(x)}{x^2}e^{-ikx}dx$ for $k\in[0,2]$

Contour integral of $\displaystyle\oint_{c} \frac{e^{ix}}{1+z^{2}} dz$

Complex integral of $\lvert z-i\rvert$ along a line

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