List questions from cauchy-integral-formula

Published on 20 May 2016 - 12:58

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Some of the Cauchy type integral property

Published on 21 May 2016 - 18:38

125

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From $ \oint \frac{\phi(t)}{t - z} dt = 0$ prove that $ \oint \frac{t \phi(t)}{t - z} dt = 0$

Published on 22 May 2016 - 18:29

1.8k

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Evaluation of the principal value of $\int\limits_{-\infty}^\infty \frac{\sin 2x}{x^3} \, dx$

Published on 26 Mar 2026 - 1:25

144

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Can I integrate this without using Cauchy's integral formula

Published on 31 May 2016 - 14:17

362

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How to integrate $\frac{\sin(z)}{(z^2 + 1/2)^2}$ over the unit circle?

Published on 02 Jun 2016 - 23:13

377

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Singularities of $z\mapsto\frac{z}{\mathrm e^z-1}$ and the Bernoulli numbers of its expansion

Published on 27 Mar 2026 - 4:23

183

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Simple Contour Integral

Published on 24 Jun 2016 - 22:27

488

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Different versions of Cauchy's integral formula and the $\overline{\partial}$ question

Published on 01 Jul 2016 - 16:36

114

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Corollary from Cauchy's integral formula

Published on 14 Apr 2017 - 11:55

482

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If $f $ is an entire function and $\displaystyle{\lim_{z \to \infty} \frac{f(z)}{z} = 0}$, prove that $f$ is constant.

Published on 15 Apr 2017 - 18:06

724

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Laurent series for $\exp(-1/z)\sin(1/z)$ at $z=0$

Published on 17 Apr 2017 - 20:55

46

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Cauchy's Integral forumla problem

Published on 23 Apr 2017 - 15:43

611

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How to calculate an integral using Cauchy's theorem?

Published on 23 Apr 2017 - 16:16

194

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A Cauchy Transform characterization for certain analytic functions on the upper plane

Published on 24 Apr 2017 - 16:54

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Inequality with analytic functions on the unit ball

Some of the Cauchy type integral property

From $ \oint \frac{\phi(t)}{t - z} dt = 0$ prove that $ \oint \frac{t \phi(t)}{t - z} dt = 0$

Evaluation of the principal value of $\int\limits_{-\infty}^\infty \frac{\sin 2x}{x^3} \, dx$

Can I integrate this without using Cauchy's integral formula

How to integrate $\frac{\sin(z)}{(z^2 + 1/2)^2}$ over the unit circle?

Singularities of $z\mapsto\frac{z}{\mathrm e^z-1}$ and the Bernoulli numbers of its expansion

Simple Contour Integral

Different versions of Cauchy's integral formula and the $\overline{\partial}$ question

Corollary from Cauchy's integral formula

If $f $ is an entire function and $\displaystyle{\lim_{z \to \infty} \frac{f(z)}{z} = 0}$, prove that $f$ is constant.

Laurent series for $\exp(-1/z)\sin(1/z)$ at $z=0$

Cauchy's Integral forumla problem

How to calculate an integral using Cauchy's theorem?

A Cauchy Transform characterization for certain analytic functions on the upper plane

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