Question

Contour Integration -- Complex Analysis

score 81 · Answer 1 · 2026-04-09 12:11:07

81

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Contour Integration -- Complex Analysis

Published on 09 Apr 2026 - 12:11

score 2.2k · Answer 2 · 2026-04-09 03:01:09

2.2k

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Contour integral with two branch cuts

Published on 09 Apr 2026 - 3:01

score 1k · Answer 3 · 2026-04-14 16:15:14

1k

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Prove $f(z)=\int_{[0,1]}\frac{1}{1-wz}dw$ is holomorphic in the open unit disk.

Published on 14 Apr 2026 - 16:15

score 459 · Answer 4 · 2026-04-11 23:38:35

459

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Conjectured value of a difficult integral with Dedekind eta functions

Published on 11 Apr 2026 - 23:38

score 1.3k · Answer 5 · 2026-04-16 07:06:23

1.3k

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Show that $\int\nolimits^{\infty}_{0} x^{-1} \sin x dx = \frac\pi2$

Published on 16 Apr 2026 - 7:06

score 4k · Answer 6 · 2026-04-13 23:17:28

4k

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Tricky contour integral resulting from the integration of $\sin ax / (x^2+b^2)$ over the positive halfline

Published on 13 Apr 2026 - 23:17

score 4.1k · Answer 7 · 2026-04-11 13:01:52

4.1k

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Calculating the Fourier transform of $\frac{\sinh(kx)}{\sinh(x)}$

Published on 11 Apr 2026 - 13:01

score 3.9k · Answer 8 · 2026-04-10 17:23:45

3.9k

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Contour Integration and Branch Cuts: $\oint_{|\omega|=x}d\omega\:(1-\omega)^{-3/4}(x-\omega)^{-3/4}\omega^{-3/4}$

Published on 10 Apr 2026 - 17:23

score 310 · Answer 9 · 2026-04-15 18:39:36

310

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Evaluation of the integral $\int_0^\infty \left(\frac{\pi^2}{4}-x^2\right)^{-2}\cdot\frac{\pi^2}{4}\cos^2 x\,dx$

Published on 15 Apr 2026 - 18:39

score 1.2k · Answer 10 · 2026-04-15 22:14:46

1.2k

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Evaluation of $\int_0^\infty \frac{x^2}{1+x^5} \mathrm{d} x$ by contour integration

Published on 15 Apr 2026 - 22:14

score 2.9k · Answer 11 · 2026-04-13 14:47:49

2.9k

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Calculating the residues of $f(z)=\frac{e^{az}}{1+e^z}$

Published on 13 Apr 2026 - 14:47

score 1.2k · Answer 12 · 2026-04-10 01:56:02

1.2k

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Proper application of Cauchy integral formula

Published on 10 Apr 2026 - 1:56

score 1.7k · Answer 13 · 2026-04-15 11:58:58

1.7k

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What contour should be used to evaluate $\int_0^\infty \frac{\sqrt{t}}{1+t^2} dt$

Published on 15 Apr 2026 - 11:58

score 4.1k · Answer 14 · 2026-04-10 23:33:30

4.1k

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Complex Analysis: Laurent Expansion for $\frac{1}{\sin(z)}$ on different annuli.

Published on 10 Apr 2026 - 23:33

score 299 · Answer 15 · 2026-04-10 09:56:41

299

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The sum of a series to be found by looking at a complex function.

Published on 10 Apr 2026 - 9:56

List Question

Contour Integration -- Complex Analysis

Contour integral with two branch cuts

Prove $f(z)=\int_{[0,1]}\frac{1}{1-wz}dw$ is holomorphic in the open unit disk.

Conjectured value of a difficult integral with Dedekind eta functions

Show that $\int\nolimits^{\infty}_{0} x^{-1} \sin x dx = \frac\pi2$

Tricky contour integral resulting from the integration of $\sin ax / (x^2+b^2)$ over the positive halfline

Calculating the Fourier transform of $\frac{\sinh(kx)}{\sinh(x)}$

Contour Integration and Branch Cuts: $\oint_{|\omega|=x}d\omega\:(1-\omega)^{-3/4}(x-\omega)^{-3/4}\omega^{-3/4}$

Evaluation of the integral $\int_0^\infty \left(\frac{\pi^2}{4}-x^2\right)^{-2}\cdot\frac{\pi^2}{4}\cos^2 x\,dx$

Evaluation of $\int_0^\infty \frac{x^2}{1+x^5} \mathrm{d} x$ by contour integration

Calculating the residues of $f(z)=\frac{e^{az}}{1+e^z}$

Proper application of Cauchy integral formula

What contour should be used to evaluate $\int_0^\infty \frac{\sqrt{t}}{1+t^2} dt$

Complex Analysis: Laurent Expansion for $\frac{1}{\sin(z)}$ on different annuli.

The sum of a series to be found by looking at a complex function.

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