List questions from cauchy-integral-formula

Published on 25 Mar 2026 - 7:47

60

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When do I know I need to use Cauchy's Integral or Cauchy's Theorem?

Published on 25 Mar 2026 - 7:43

111

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Contour Integration cauchy integration formula

Published on 25 Mar 2026 - 9:22

238

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Definite integral involving a log and a rational function.

Published on 29 Apr 2026 - 12:53

68

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Prove the following equality involving $f'(0)$

Published on 25 Mar 2026 - 7:48

74

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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 25 Mar 2026 - 7:44

295

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Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Published on 25 Mar 2026 - 7:45

70

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Yet some other integrals containing an inverse trigonometric and a rational function.

Published on 29 Apr 2026 - 12:53

280

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Gaussian integral over a wedge of the complex plane

Published on 25 Mar 2026 - 1:16

53

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Contour integration with a complex variable

Published on 25 Mar 2026 - 9:22

194

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Contour integral on closed contour C that contains a singularity

Published on 25 Mar 2026 - 7:42

262

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Closed contour integral that contains singularities

Published on 25 Mar 2026 - 7:41

86

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Evaluate function using Cauchy's integral formula

Published on 25 Mar 2026 - 9:22

42

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Complex integration using Cauchy Goursat (I think)

Published on 24 Mar 2026 - 23:53

181

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complex integral over a closed path.

Published on 06 Apr 2026 - 5:30

List Question

Having trouble evaluating this integral using the binomial theorem.

When do I know I need to use Cauchy's Integral or Cauchy's Theorem?

Contour Integration cauchy integration formula

Definite integral involving a log and a rational function.

Prove the following equality involving $f'(0)$

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

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Yet some other integrals containing an inverse trigonometric and a rational function.

Gaussian integral over a wedge of the complex plane

Contour integration with a complex variable

Contour integral on closed contour C that contains a singularity

Closed contour integral that contains singularities

Evaluate function using Cauchy's integral formula

Complex integration using Cauchy Goursat (I think)

complex integral over a closed path.

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