List questions from cauchy-integral-formula

288

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Proving:$\frac{1}{2i}\int\limits_{-\infty}^{\infty}\frac{e^{ix}-1}{x}dx = \frac{\pi}{2}$ via Complex Methods?

Published on 23 May 2017 - 22:21

334

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Is there connection between Stieltjes transformation and Cauchy integral formula?

Published on 26 May 2017 - 22:17

63

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Proof $\lim_{r\to 0}\int_{C_r} f(z)dz=iA\alpha$

Published on 29 May 2017 - 3:41

820

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Bounding the derivative of a function

Published on 31 May 2017 - 18:12

1.4k

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Uniform limits of derivative of analytic function

Published on 02 Jun 2017 - 19:40

3.5k

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Problem with elementary complex integration of $1/(z-1)$

Published on 08 Jun 2017 - 17:16

112

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Calculate $\int_C (\cos(z)+i) \, dz$ along the path $z(\theta) = \tfrac{\pi}{4} e^{i \theta}$, $\theta \in [0,\pi]$

Published on 16 Jun 2017 - 16:46

161

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Complex integral $\oint\frac{\sin(\pi i z/2)}{z^2-(i+1)z+i}dz$ on the circle with center $i/2$ and radius $1$

Published on 18 Jun 2017 - 11:26

350

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Calculating a complex integral with generalized Cauchy integral formula

Published on 20 Jun 2017 - 15:51

379

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$\int_{-\infty}^{\infty} \frac{1}{x^2 +2} \, dx$

Published on 21 Jun 2017 - 2:41

431

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Use of Extended Cauchy Integral Formula

Published on 21 Jun 2017 - 9:24

41

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Relevant Singularities.

Published on 23 Jun 2017 - 19:01

562

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Evaluate $\int_0^1 \frac{dx}{(x^2-x^3)^\frac13}$ using contour integration

Published on 24 Jun 2017 - 1:10

1.2k

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Show that sum of residues of $f(z)$ at it's poles is equal to $\frac{a_{n-1}}{b_n}$ where

Published on 24 Jun 2017 - 6:15

376

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Significance of the Triangle Inequality

Published on 25 Jun 2017 - 9:44

List Question

Proving:$\frac{1}{2i}\int\limits_{-\infty}^{\infty}\frac{e^{ix}-1}{x}dx = \frac{\pi}{2}$ via Complex Methods?

Is there connection between Stieltjes transformation and Cauchy integral formula?

Proof $\lim_{r\to 0}\int_{C_r} f(z)dz=iA\alpha$

Bounding the derivative of a function

Uniform limits of derivative of analytic function

Problem with elementary complex integration of $1/(z-1)$

Calculate $\int_C (\cos(z)+i) \, dz$ along the path $z(\theta) = \tfrac{\pi}{4} e^{i \theta}$, $\theta \in [0,\pi]$

Complex integral $\oint\frac{\sin(\pi i z/2)}{z^2-(i+1)z+i}dz$ on the circle with center $i/2$ and radius $1$

Calculating a complex integral with generalized Cauchy integral formula

$\int_{-\infty}^{\infty} \frac{1}{x^2 +2} \, dx$

Use of Extended Cauchy Integral Formula

Relevant Singularities.

Evaluate $\int_0^1 \frac{dx}{(x^2-x^3)^\frac13}$ using contour integration

Show that sum of residues of $f(z)$ at it's poles is equal to $\frac{a_{n-1}}{b_n}$ where

Significance of the Triangle Inequality

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