Question

How to prove $\lim\limits_{t \to 1^-} \frac{\sqrt{1-t^2}}{2\pi}\int_{S^1}\frac{f(x,y)}{1-tx}ds=f(1,0)$?

score 83 · Answer 1 · 2014-12-18 02:39:23

83

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How to prove $\lim\limits_{t \to 1^-} \frac{\sqrt{1-t^2}}{2\pi}\int_{S^1}\frac{f(x,y)}{1-tx}ds=f(1,0)$?

Published on 18 Dec 2014 - 2:39

score 192 · Answer 2 · 2014-12-18 11:44:20

192

Views

Two different results with contour integration: $I = \int_\mathbb R \frac 1 {(3x-2i)^2} dx $

Published on 18 Dec 2014 - 11:44

score 111 · Answer 3 · 2026-03-29 04:48:16

111

Views

When should I resort to Eulers identity?

Published on 29 Mar 2026 - 4:48

score 319 · Answer 4 · 2014-12-21 19:27:24

319

Views

difficult complex integral $\int_\gamma \frac{1}{z^2+i}dz$

Published on 21 Dec 2014 - 19:27

score 625 · Answer 5 · 2014-12-22 12:45:31

625

Views

Choosing a contour to integrate over.

Published on 22 Dec 2014 - 12:45

score 1k · Answer 6 · 2014-12-22 13:12:56

1k

Views

Evaluation of $\int_{0}^{\infty} \cos(x)/(x^2+1)$ using complex analysis.

Published on 22 Dec 2014 - 13:12

score 1.5k · Answer 7 · 2026-03-31 19:15:04

1.5k

Views

finding the inverse Laplace transform of $\frac{1}{z\sqrt{z+1}}$

Published on 31 Mar 2026 - 19:15

score 130 · Answer 8 · 2026-03-29 05:43:36

130

Views

how to calculate the following integral$\int_{-\infty}^{\infty}\frac{1}{\left(t^2+\pi^2\right)^2 \cosh(t)}dt$

Published on 29 Mar 2026 - 5:43

score 199 · Answer 9 · 2014-12-23 10:32:35

199

Views

Solving an integral using a keyhole based integral (text given)

Published on 23 Dec 2014 - 10:32

score 496 · Answer 10 · 2014-12-23 19:36:28

496

Views

How many poles have to be inside the contour?

Published on 23 Dec 2014 - 19:36

score 2.9k · Answer 11 · 2014-12-23 19:49:17

2.9k

Views

Contour integration when pole is outside the contour

Published on 23 Dec 2014 - 19:49

score 806 · Answer 12 · 2026-03-29 08:15:56

806

Views

Transformation of contour integral $\int \frac{z^2}{e^{2\pi i z^3}-1} \operatorname dz$ over the circle $|z|=\sqrt[3]{n+\frac{1}{2}}$

Published on 29 Mar 2026 - 8:15

score 276 · Answer 13 · 2014-12-24 09:17:52

276

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Planning to integrate $\int_{0}^{\infty} \frac{\log^2(x)}{x^2 + 1} dx$ using complex analysis

Published on 24 Dec 2014 - 9:17

score 851 · Answer 14 · 2014-12-24 12:14:31

851

Views

How to show the contour integral goes to $0$ of semicircle?

Published on 24 Dec 2014 - 12:14

score 1.8k · Answer 15 · 2014-12-24 12:52:53

1.8k

Views

Integral with contour integration: $\int_{-\infty}^{0}\frac{2x^2-1}{x^4+1}\,dx$

Published on 24 Dec 2014 - 12:52

List Question

How to prove $\lim\limits_{t \to 1^-} \frac{\sqrt{1-t^2}}{2\pi}\int_{S^1}\frac{f(x,y)}{1-tx}ds=f(1,0)$?

Two different results with contour integration: $I = \int_\mathbb R \frac 1 {(3x-2i)^2} dx $

When should I resort to Eulers identity?

difficult complex integral $\int_\gamma \frac{1}{z^2+i}dz$

Choosing a contour to integrate over.

Evaluation of $\int_{0}^{\infty} \cos(x)/(x^2+1)$ using complex analysis.

finding the inverse Laplace transform of $\frac{1}{z\sqrt{z+1}}$

how to calculate the following integral$\int_{-\infty}^{\infty}\frac{1}{\left(t^2+\pi^2\right)^2 \cosh(t)}dt$

Solving an integral using a keyhole based integral (text given)

How many poles have to be inside the contour?

Contour integration when pole is outside the contour

Transformation of contour integral $\int \frac{z^2}{e^{2\pi i z^3}-1} \operatorname dz$ over the circle $|z|=\sqrt[3]{n+\frac{1}{2}}$

Planning to integrate $\int_{0}^{\infty} \frac{\log^2(x)}{x^2 + 1} dx$ using complex analysis

How to show the contour integral goes to $0$ of semicircle?

Integral with contour integration: $\int_{-\infty}^{0}\frac{2x^2-1}{x^4+1}\,dx$

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