List questions from cauchy-integral-formula

Published on 20 Mar 2026 - 9:13

59

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

Published on 19 Mar 2026 - 20:46

110

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Contour Integration cauchy integration formula

Published on 22 Mar 2026 - 18:07

232

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Definite integral involving a log and a rational function.

Published on 22 Mar 2026 - 23:05

67

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

Published on 22 Mar 2026 - 16:01

73

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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 20 Mar 2026 - 16:03

294

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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 20 Mar 2026 - 0:59

64

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

Published on 23 Mar 2026 - 13:52

280

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Gaussian integral over a wedge of the complex plane

Published on 25 Mar 2026 - 1:16

52

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Contour integration with a complex variable

Published on 22 Mar 2026 - 7:41

193

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Contour integral on closed contour C that contains a singularity

Published on 20 Mar 2026 - 4:16

261

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Closed contour integral that contains singularities

Published on 22 Mar 2026 - 16:56

85

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Evaluate function using Cauchy's integral formula

Published on 22 Mar 2026 - 20:10

42

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Complex integration using Cauchy Goursat (I think)

Published on 24 Mar 2026 - 23:53

179

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complex integral over a closed path.

Published on 22 Mar 2026 - 4:46

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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