Question

A question about Cauchy Integral Theorem.

score 458 · Answer 1 · 2026-04-12 03:07:24

458

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A question about Cauchy Integral Theorem.

Published on 12 Apr 2026 - 3:07

score 1.2k · Answer 2 · 2026-04-15 12:04:45

1.2k

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Evaluate the integral $\int_C f(z)dz$ where $C$ is the unit circle centered at the origin with $f(z) = e^{iz}/(z-a)$, $0<a<1$?

Published on 15 Apr 2026 - 12:04

score 150 · Answer 3 · 2026-04-29 12:21:56

150

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Evaluate $\frac{1}{2\pi i}\int_\gamma\frac{f(z)}{(z-z_1)(z-z_2)}-\frac{f(z)}{(z-z_0)^2}$

Published on 29 Apr 2026 - 12:21

score 151 · Answer 4 · 2026-04-15 06:45:26

151

Views

Proving $g'(z)=\frac{1}{2\pi{}i}\int_{C}\frac{g(u)du}{(u-z)^2}$ for $g(z)$ holomorphic in and on contour $C$, and $z$ in $C$'s interior

Published on 15 Apr 2026 - 6:45

score 153 · Answer 5 · 2026-04-08 19:54:44

153

Views

Wirtinger derivatives and Cauchy integral

Published on 08 Apr 2026 - 19:54

score 282 · Answer 6 · 2026-04-08 16:11:54

282

Views

Mean value theorem for a disk (complex analysis)

Published on 08 Apr 2026 - 16:11

score 107 · Answer 7 · 2026-04-09 18:59:47

107

Views

Question about Domain and the Open Disk in Cauchy's Integral Formula

Published on 09 Apr 2026 - 18:59

score 138 · Answer 8 · 2026-04-09 11:37:41

138

Views

Using Cauchy Integral Formula To Solve Integrals

Published on 09 Apr 2026 - 11:37

score 265 · Answer 9 · 2026-04-13 21:11:19

265

Views

On singularity of limit holomorphic function

Published on 13 Apr 2026 - 21:11

score 369 · Answer 10 · 2026-04-16 20:51:25

369

Views

Entire function such that $\lim_{ z \to \infty} \frac{f(z)}{z^N} = 0$ then $f$ is a polynomial of degree at most $N$.

Published on 16 Apr 2026 - 20:51

score 52 · Answer 11 · 2026-04-12 20:15:03

52

Views

Cauchy's integral formula "type" integral

Published on 12 Apr 2026 - 20:15

score 40 · Answer 12 · 2026-04-13 17:45:03

40

Views

Have I evaluated this complex integral correctly?

Published on 13 Apr 2026 - 17:45

score 430 · Answer 13 · 2026-04-15 10:54:18

430

Views

If a seq of holomorphic function on an open set $\Omega$, $\{f_n\}$ coverges uniformly to a function $f$ on every compact set then so does $f_n'$

Published on 15 Apr 2026 - 10:54

score 73 · Answer 14 · 2026-04-12 04:14:29

73

Views

Nested integral with same function at every integral being multiplied an integrated again.

Published on 12 Apr 2026 - 4:14

score 903 · Answer 15 · 2026-04-15 02:56:47

903

Views

Using Cauchy Integral Formula for $ \oint \frac{\cos(z)}{z(z^2+8)} $ on curve |z| =2

Published on 15 Apr 2026 - 2:56

List Question

A question about Cauchy Integral Theorem.

Evaluate the integral $\int_C f(z)dz$ where $C$ is the unit circle centered at the origin with $f(z) = e^{iz}/(z-a)$, $0<a<1$?

Evaluate $\frac{1}{2\pi i}\int_\gamma\frac{f(z)}{(z-z_1)(z-z_2)}-\frac{f(z)}{(z-z_0)^2}$

Proving $g'(z)=\frac{1}{2\pi{}i}\int_{C}\frac{g(u)du}{(u-z)^2}$ for $g(z)$ holomorphic in and on contour $C$, and $z$ in $C$'s interior

Wirtinger derivatives and Cauchy integral

Mean value theorem for a disk (complex analysis)

Question about Domain and the Open Disk in Cauchy's Integral Formula

Using Cauchy Integral Formula To Solve Integrals

On singularity of limit holomorphic function

Entire function such that $\lim_{ z \to \infty} \frac{f(z)}{z^N} = 0$ then $f$ is a polynomial of degree at most $N$.

Cauchy's integral formula "type" integral

Have I evaluated this complex integral correctly?

If a seq of holomorphic function on an open set $\Omega$, $\{f_n\}$ coverges uniformly to a function $f$ on every compact set then so does $f_n'$

Nested integral with same function at every integral being multiplied an integrated again.

Using Cauchy Integral Formula for $ \oint \frac{\cos(z)}{z(z^2+8)} $ on curve |z| =2

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