List questions from complex-integration

Published on 16 Oct 2021 - 21:46

129

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Show that the function $f(z) = 1/(z-4)$ has an antiderivative in a Domain that contains the the Unit Circle (where the Unit circle is a contour)

Published on 17 Oct 2021 - 3:04

43

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Integral Computation - Error Functions

Published on 29 Mar 2026 - 19:07

108

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Prove $|e^{z^2+1}| \le e^2$

Published on 31 Mar 2026 - 5:38

330

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Setup complex line integral $\int_{\gamma}x^2+y^2 dz$, where $\gamma$ is the line segment from $i+2$ to $-i-1$

Published on 31 Mar 2026 - 3:38

161

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Contour Integral of $z \hspace{0.5mm} \exp(z^2)\,dz$

Published on 24 Oct 2021 - 12:08

61

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Evaluating $\int_{\gamma}z^2e^{z^3}dz$

Published on 31 Mar 2026 - 3:37

112

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$\int_0^{2\pi}\cos^n\theta\,d\theta$ by integration in the complex plane

Published on 29 Mar 2026 - 23:59

640

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Exercise 2.11 from Stein's Complex Analysis

Published on 26 Oct 2021 - 22:21

194

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Contour integration for $\int_0^\infty \frac{x^{\alpha -1}}{(x+\beta)(x+\gamma)}dx$

Published on 27 Oct 2021 - 15:23

42

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Find integral of $f:D\to \mathbb{C}$ where $f$ is a branch of square root with $f(1)=-1$

Published on 27 Oct 2021 - 20:31

32

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Complex Integration of Improper Integrals

Published on 28 Oct 2021 - 4:19

76

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Integrating over curve of constant modulus

Published on 29 Oct 2021 - 4:33

129

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Proving $\sum_{n=1}^\infty \frac{1}{(n^2+a^2)^2}=\frac{\pi}{4a^3}\left[\coth(\pi a)+\frac{\pi a}{\sinh^2 \pi a}-\frac{2}{\pi a}\right]$

Published on 30 Oct 2021 - 10:05

30

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How to evaluate this complex integral on this particular contour?

Published on 09 Apr 2026 - 7:22

List Question

Property of Beta function: $|B(a,b)|\le B(\Re(a),\Re(b))$

Show that the function $f(z) = 1/(z-4)$ has an antiderivative in a Domain that contains the the Unit Circle (where the Unit circle is a contour)

Integral Computation - Error Functions

Prove $|e^{z^2+1}| \le e^2$

Setup complex line integral $\int_{\gamma}x^2+y^2 dz$, where $\gamma$ is the line segment from $i+2$ to $-i-1$

Contour Integral of $z \hspace{0.5mm} \exp(z^2)\,dz$

Evaluating $\int_{\gamma}z^2e^{z^3}dz$

$\int_0^{2\pi}\cos^n\theta\,d\theta$ by integration in the complex plane

Exercise 2.11 from Stein's Complex Analysis

Contour integration for $\int_0^\infty \frac{x^{\alpha -1}}{(x+\beta)(x+\gamma)}dx$

Find integral of $f:D\to \mathbb{C}$ where $f$ is a branch of square root with $f(1)=-1$

Complex Integration of Improper Integrals

Integrating over curve of constant modulus

Proving $\sum_{n=1}^\infty \frac{1}{(n^2+a^2)^2}=\frac{\pi}{4a^3}\left[\coth(\pi a)+\frac{\pi a}{\sinh^2 \pi a}-\frac{2}{\pi a}\right]$

How to evaluate this complex integral on this particular contour?

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