List questions from complex-integration

Published on 08 May 2021 - 14:31

457

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Applying Cauchy-Goursat Theorem

Published on 29 Mar 2026 - 18:35

106

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Prinicipal value integral of $\exp(iaz)/z$

Published on 09 May 2021 - 16:38

191

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Solve the integral $\int^{+\infty}_0\frac{x\sin x}{1+x^4}dx$ using complex analysis

Published on 29 Mar 2026 - 18:31

151

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Residue Theorem and improper integrals

Published on 10 May 2021 - 20:54

387

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Prove that $\lim_{r\to 0}\int\frac{f(z)}{z-a}dz=2\pi i f(a)$

Published on 30 Mar 2026 - 13:41

338

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Hints for contour integration of $\int_0^\infty \frac{x^{1/3}}{x^4+1}dx$

Published on 11 May 2021 - 19:18

16

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Problems met in mastsubara frequency sum

Published on 08 Apr 2026 - 13:36

71

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Complex integrals and poles

Published on 13 May 2021 - 18:07

34

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Calculate a complex integral by its residues

Published on 28 Mar 2026 - 11:54

103

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Evaluating $\int_c \cot^2z $ dz

Published on 14 May 2021 - 4:17

198

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Integrating $\int_{0}^{\infty}\frac{\cos(x)}{(1+x^2)^2}dx$ without the residue theorem?

Published on 14 May 2021 - 8:37

172

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Where is my mistake in calculating the Fresnel integral?

Published on 08 Apr 2026 - 16:49

100

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$\int_{C(i,2)}^{}\frac{1}{(z^2+4)^2}\: dz $ (verification)

Published on 14 May 2021 - 18:47

53

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Calculate using residues $\oint\limits_\gamma\frac{\tan z}{z + 2}dz$, where $\gamma: |z + 2| = 2$ - a closed loop, run counterclockwise.

Published on 14 May 2021 - 20:33

List Question

contour integral with a singularity of a fractional power

Applying Cauchy-Goursat Theorem

Prinicipal value integral of $\exp(iaz)/z$

Solve the integral $\int^{+\infty}_0\frac{x\sin x}{1+x^4}dx$ using complex analysis

Residue Theorem and improper integrals

Prove that $\lim_{r\to 0}\int\frac{f(z)}{z-a}dz=2\pi i f(a)$

Hints for contour integration of $\int_0^\infty \frac{x^{1/3}}{x^4+1}dx$

Problems met in mastsubara frequency sum

Complex integrals and poles

Calculate a complex integral by its residues

Evaluating $\int_c \cot^2z $ dz

Integrating $\int_{0}^{\infty}\frac{\cos(x)}{(1+x^2)^2}dx$ without the residue theorem?

Where is my mistake in calculating the Fresnel integral?

$\int_{C(i,2)}^{}\frac{1}{(z^2+4)^2}\: dz $ (verification)

Calculate using residues $\oint\limits_\gamma\frac{\tan z}{z + 2}dz$, where $\gamma: |z + 2| = 2$ - a closed loop, run counterclockwise.

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