List questions from complex-integration

Published on 03 Jun 2019 - 15:34

138

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Does the Argument Principle for Winding Numbers have an Area Integral Analog (by Stokes' Theorem)?

Published on 26 Mar 2026 - 6:28

63

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Computing $\int_{|z|=\frac{2}{3}}\frac{\sin z}{z e^{\frac{1}{z+2}}}$

Published on 04 Jun 2019 - 13:25

485

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Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$

Published on 04 Jun 2019 - 13:50

84

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if $\sup_{0<r<1} \int_0^{2\pi} |f(re^{i t})|^2 dt < \infty$ then $\sum{|a_n|^2} <\infty$

Published on 25 Mar 2026 - 20:36

90

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Why is $1/2 \int_{- \infty}^{\infty} \frac{\cos(x)}{(1+x^2)^{2}} dx = \frac{\pi}{2e} $ and not $\frac{\pi}{4e}$

Published on 06 Jun 2019 - 10:37

61

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The value of $I=\int_{|z|=2}z^2\sin\frac{1}{z}dz$?

Published on 06 Jun 2019 - 13:58

511

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Why does the definite integral of $\frac{\cos(x)}{\sqrt{x}}$ converge

Published on 07 Jun 2019 - 3:45

828

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Computing $\int_{|z|=1}z^3\sin(\frac{1}{z})dz$ and $\int_{|z|=\frac{2}{3}}\sin(\frac{1}{z^2}+e^{z^2}\cos(z))dz $

Published on 07 Jun 2019 - 14:13

142

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Is $\int_{|z|=2}\exp\bigl(e^{1/z}\bigr)\,dz = 2\pi ie$?

Published on 08 Jun 2019 - 6:46

62

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how to prove this integral

Published on 08 Jun 2019 - 9:51

618

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Solve complex integral of $1/(z^5+1)$

Published on 09 Jun 2019 - 12:10

76

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Morera's theorem: A holomorphic function on $D\backslash\mathbb R$ is already holomorphic on $D$.

Published on 11 Jun 2019 - 19:49

1k

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What is $ \dfrac{i}{4-π} \int_{|z|=4} \dfrac{dz}{z \cos z}$?

Published on 25 Mar 2026 - 22:05

397

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Show that $z^5 - z +16$ has two roots in the right half plane

Published on 24 Mar 2026 - 23:46

List Question

complex integration paths

Does the Argument Principle for Winding Numbers have an Area Integral Analog (by Stokes' Theorem)?

Computing $\int_{|z|=\frac{2}{3}}\frac{\sin z}{z e^{\frac{1}{z+2}}}$

Integral $\small \int_0^\infty \frac{(\pi x - 2\log{x})^3}{\left(\log^2{x} + \frac{\pi^2}{4}\right)(1+x^2)^2} \text{d}x$

if $\sup_{0<r<1} \int_0^{2\pi} |f(re^{i t})|^2 dt < \infty$ then $\sum{|a_n|^2} <\infty$

Why is $1/2 \int_{- \infty}^{\infty} \frac{\cos(x)}{(1+x^2)^{2}} dx = \frac{\pi}{2e} $ and not $\frac{\pi}{4e}$

The value of $I=\int_{|z|=2}z^2\sin\frac{1}{z}dz$?

Why does the definite integral of $\frac{\cos(x)}{\sqrt{x}}$ converge

Computing $\int_{|z|=1}z^3\sin(\frac{1}{z})dz$ and $\int_{|z|=\frac{2}{3}}\sin(\frac{1}{z^2}+e^{z^2}\cos(z))dz $

Is $\int_{|z|=2}\exp\bigl(e^{1/z}\bigr)\,dz = 2\pi ie$?

how to prove this integral

Solve complex integral of $1/(z^5+1)$

Morera's theorem: A holomorphic function on $D\backslash\mathbb R$ is already holomorphic on $D$.

What is $ \dfrac{i}{4-π} \int_{|z|=4} \dfrac{dz}{z \cos z}$?

Show that $z^5 - z +16$ has two roots in the right half plane

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