List questions from complex-integration

Published on 10 May 2026 - 14:30

155

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Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$

Published on 16 Apr 2026 - 8:14

139

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Having trouble evaluating this integral using the binomial theorem.

Published on 10 May 2026 - 15:27

238

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Evaluating a tricky integral using Cauchy's integral formula.

Published on 08 Apr 2026 - 21:08

107

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Computing $\beta(\frac{1}{m},\frac{1}{m})$

Published on 16 Apr 2026 - 12:25

144

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Evaluating Trig Integrals with Residues

Published on 12 Apr 2026 - 7:55

129

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Calculate the following contour integrals $\int_{\lambda}\overline z dz$ and $ \int_{\lambda}e^zdz$

Published on 14 Apr 2026 - 2:29

1.5k

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Complex Exponential Function Integration

Published on 11 Apr 2026 - 6:51

46

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Is there any complex integral that is singular and cannot be solved using residue theorems?

Published on 11 Apr 2026 - 7:31

100

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$\int_\gamma\frac{1}{|\xi-z|}\,d|\xi|=2\pi$?

Published on 15 Apr 2026 - 3:11

95

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Evaluating real integrals through residues

Published on 12 Apr 2026 - 2:48

181

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Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$

Published on 16 Apr 2026 - 13:15

96

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The possible values of the $\frac{1}{2\pi i}\int_\gamma \frac{e^z}{(z-1)(z-2)}$

Published on 15 Apr 2026 - 18:59

32

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Numerically Verify Complex Integrals

Published on 11 Apr 2026 - 5:49

75

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Showing that $\sum\limits_{l=0}^\infty \frac{1}{(3l+2)!}=\frac{1}{3}(e-\frac{2}{\sqrt{e}} \cos(\frac{\pi}{3}-\frac{\sqrt{3}}{2}))$

Published on 10 May 2026 - 15:30

List Question

Verifying inverse Fourier's Transform using Cauchy's integral formula

Showing that $\frac{1}{2\pi}\int^{2\pi}_{0}(2\cos\theta)^{2n}d\theta=\frac{(2n)!}{n!n!}$

Having trouble evaluating this integral using the binomial theorem.

Evaluating a tricky integral using Cauchy's integral formula.

Computing $\beta(\frac{1}{m},\frac{1}{m})$

Evaluating Trig Integrals with Residues

Calculate the following contour integrals $\int_{\lambda}\overline z dz$ and $ \int_{\lambda}e^zdz$

Complex Exponential Function Integration

Is there any complex integral that is singular and cannot be solved using residue theorems?

$\int_\gamma\frac{1}{|\xi-z|}\,d|\xi|=2\pi$?

Evaluating real integrals through residues

Integrating $\int_0^{2\pi} \frac1{a\cos(t)+b\sin(t)+c}dt$ with $\sqrt{a^2+b^2}=1<c$

The possible values of the $\frac{1}{2\pi i}\int_\gamma \frac{e^z}{(z-1)(z-2)}$

Numerically Verify Complex Integrals

Showing that $\sum\limits_{l=0}^\infty \frac{1}{(3l+2)!}=\frac{1}{3}(e-\frac{2}{\sqrt{e}} \cos(\frac{\pi}{3}-\frac{\sqrt{3}}{2}))$

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