List questions from contour-integration

Published on 17 Apr 2026 - 12:43

114

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Residue theorem for $ I=\int_{-\infty}^{+\infty}\frac{e^{\mathrm{i}\,t\,z}}{(z-z_1)(z-z_2)} \, \mathrm{d}z$

Published on 16 Apr 2026 - 12:33

163

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Inverse Laplace transform of $\frac{\coth(s)}{s^2}$

Published on 15 Apr 2026 - 21:11

93

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Two functions under one closed line integral

Published on 11 Apr 2026 - 12:17

428

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Cauchy Principal Value of $\int_{-\infty}^\infty \frac{e^{ipx}}{x^4-1}\,\mathrm{d}x$

Published on 26 Mar 2026 - 3:12

82

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Where did I go wrong with this Bromwich integral?

Published on 13 Apr 2026 - 15:04

43

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Contour integral in terms of unknown function

Published on 09 Apr 2026 - 14:15

677

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Residue Theorem Integral of $\frac{1}{\sinh(x)-1}$

Published on 15 Apr 2026 - 19:18

55

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Show that $\int_0^\infty \frac{\log x}{\prod_{u=0}^n (1+\alpha_u\,x)}\,dx = ...$

Published on 17 Apr 2026 - 2:55

37

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Steepest descent with slow variation

Published on 12 Apr 2026 - 2:18

645

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Leibniz's Rule in the Complex Domain

Published on 12 Apr 2026 - 18:08

374

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contour integration with dogbone, branch cut: $\frac1{2\pi\mathrm{i}}\int_{|z|=2}\frac{\sqrt{z^2-1}}{z-3}\,\mathrm{d}z$

Published on 17 Apr 2026 - 4:25

137

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Is there any way to tackle this integral (generating functions)?

Published on 13 Apr 2026 - 19:21

93

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Hilbert transform/contour integral $\int_{-\infty}^{\infty} \frac{\sin nx}{1-\lambda \cos x}\frac{1}{t-x} dx$

Published on 16 Apr 2026 - 9:33

61

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Modified Cauchy Integral Formula

Published on 09 Apr 2026 - 11:06

List Question

Why are $\Gamma_k$ and $\Gamma_{k+1}$ close together?

Residue theorem for $ I=\int_{-\infty}^{+\infty}\frac{e^{\mathrm{i}\,t\,z}}{(z-z_1)(z-z_2)} \, \mathrm{d}z$

Inverse Laplace transform of $\frac{\coth(s)}{s^2}$

Two functions under one closed line integral

Cauchy Principal Value of $\int_{-\infty}^\infty \frac{e^{ipx}}{x^4-1}\,\mathrm{d}x$

Where did I go wrong with this Bromwich integral?

Contour integral in terms of unknown function

Residue Theorem Integral of $\frac{1}{\sinh(x)-1}$

Show that $\int_0^\infty \frac{\log x}{\prod_{u=0}^n (1+\alpha_u\,x)}\,dx = ...$

Steepest descent with slow variation

Leibniz's Rule in the Complex Domain

contour integration with dogbone, branch cut: $\frac1{2\pi\mathrm{i}}\int_{|z|=2}\frac{\sqrt{z^2-1}}{z-3}\,\mathrm{d}z$

Is there any way to tackle this integral (generating functions)?

Hilbert transform/contour integral $\int_{-\infty}^{\infty} \frac{\sin nx}{1-\lambda \cos x}\frac{1}{t-x} dx$

Modified Cauchy Integral Formula

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