List questions from cauchy-integral-formula

Published on 01 Sep 2021 - 9:29

82

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Calcule $\int _{C} \frac{z^2}{z-1} dz$, $|z|= 2$ and $\int _{C} \frac{e^{z}}{z^{2}} dz$, $|z | = 1$, where $C$ is a circle.

Published on 02 Sep 2021 - 14:22

549

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complex contour integral with poles

Published on 10 Sep 2021 - 22:19

144

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Why does the Cauchy Integral Formula hold for when $\gamma$ is not a circle?

Published on 11 Sep 2021 - 17:59

50

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In the Cauchy Integral Formula generalisation of analytic functions to matrix functions is it acceptable to let the curve not enclose all eigenvalues?

Published on 12 Sep 2021 - 8:16

37

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Complex Integral and Cauchy's Integral Formula

Published on 12 Sep 2021 - 14:02

134

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The Cauchy Integral Formula for matrices must have $\gamma$ enclose all eigenvalues of the matrix for validity, but must it contain the origin?

Published on 14 Sep 2021 - 20:24

69

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special case of the Cauchy integral formula

Published on 19 Sep 2021 - 14:35

155

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Interesting applications of major results in complex analysis

Published on 21 Sep 2021 - 8:54

252

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An analog of the Cauchy Integral Formula

Published on 25 Sep 2021 - 18:30

143

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Complex analysis about Cauchy's integral formula

Published on 25 Sep 2021 - 22:42

463

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Proving $\oint_C \frac{f'(z)}{z-z_0}dz = \oint_C \frac{f(z)}{(z-z_0)^2}dz$

Published on 27 Sep 2021 - 3:17

58

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Calculation of residuals in Philippe Flajolet Robert Sedgewick

Published on 27 Sep 2021 - 4:05

60

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Simplifying an expression using the binomial theorem

Published on 06 Oct 2021 - 8:47

112

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Proof every holomorphic function is identically zero

Published on 06 Oct 2021 - 18:28

List Question

Complex Integral with Cauchy's Formula problem.

Calcule $\int _{C} \frac{z^2}{z-1} dz$, $|z|= 2$ and $\int _{C} \frac{e^{z}}{z^{2}} dz$, $|z | = 1$, where $C$ is a circle.

complex contour integral with poles

Why does the Cauchy Integral Formula hold for when $\gamma$ is not a circle?

In the Cauchy Integral Formula generalisation of analytic functions to matrix functions is it acceptable to let the curve not enclose all eigenvalues?

Complex Integral and Cauchy's Integral Formula

The Cauchy Integral Formula for matrices must have $\gamma$ enclose all eigenvalues of the matrix for validity, but must it contain the origin?

special case of the Cauchy integral formula

Interesting applications of major results in complex analysis

An analog of the Cauchy Integral Formula

Complex analysis about Cauchy's integral formula

Proving $\oint_C \frac{f'(z)}{z-z_0}dz = \oint_C \frac{f(z)}{(z-z_0)^2}dz$

Calculation of residuals in Philippe Flajolet Robert Sedgewick

Simplifying an expression using the binomial theorem

Proof every holomorphic function is identically zero

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