Question

$f: D\to \mathbb C$ is holomorphic such that $diam f(D)=d$, then $|f'(0)|=d/2\implies f$ is linear.

score 101 · Answer 1 · 2023-02-28 21:30:53

101

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$f: D\to \mathbb C$ is holomorphic such that $diam f(D)=d$, then $|f'(0)|=d/2\implies f$ is linear.

Published on 28 Feb 2023 - 21:30

score 65 · Answer 2 · 2026-03-25 19:04:22

65

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Does the $\Gamma\subset\mathbb{C}$ curve always has to be smooth in Cauchy's integral theorem?

Published on 25 Mar 2026 - 19:04

score 112 · Answer 3 · 2023-03-03 13:23:04

112

Views

Cauchy integral formula for a unbounded domain

Published on 03 Mar 2023 - 13:23

score 49 · Answer 4 · 2023-03-06 18:42:44

49

Views

Upper bound of a function in Hoffman and Mardsten's Complex Analysis 2.8

Published on 06 Mar 2023 - 18:42

score 64 · Answer 5 · 2023-03-06 23:48:01

64

Views

How to prove that a sum is inclosed by two upper and lower bounds (values)?

Published on 06 Mar 2023 - 23:48

score 59 · Answer 6 · 2023-03-11 18:19:48

Prove that if $f$ is holomorphic inside and on a circle of radius $R$ centered at $z_0$, then $|f(z_0)| \geq \min_{z \in C_{R}(z_0)} |f(z)|$

score 69 · Answer 7 · 2023-03-20 15:31:44

69

Views

How to show $\mathbb E[f(X)]=f(\mu +i\sigma)$ using Cauchy integral formula

Published on 20 Mar 2023 - 15:31

score 155 · Answer 8 · 2023-03-24 03:15:40

155

Views

Show that integral $\int \frac{f'(w)}{w-z} dw = \int \frac{f(w)}{(w-z)^2} dw$

Published on 24 Mar 2023 - 3:15

score 59 · Answer 9 · 2023-03-26 10:01:45

59

Views

Example for complex integral

Published on 26 Mar 2023 - 10:01

score 49 · Answer 10 · 2023-04-15 16:54:36

49

Views

Choosing a path for reverse Cauchy integral formula

Published on 15 Apr 2023 - 16:54

score 105 · Answer 11 · 2023-04-17 05:25:56

105

Views

Complex conjugate by complex integration

Published on 17 Apr 2023 - 5:25

score 91 · Answer 12 · 2023-04-21 01:39:34

91

Views

Integrating $\frac {e^{-iz}}{z}$ over a semicircle counter-clockwise around $0$ of infinite radius $r$

Published on 21 Apr 2023 - 1:39

score 29 · Answer 13 · 2023-04-23 16:26:21

29

Views

Compute integrals using Cauchy Integral Formula

Published on 23 Apr 2023 - 16:26

score 132 · Answer 14 · 2023-04-30 10:57:41

132

Views

Can this given $f: S^1\to \mathbb C$ be extended to a continuous $F: \overline{\mathbb D}\to \mathbb C, F$ is holomorphic on $\mathbb D$?

Published on 30 Apr 2023 - 10:57

score 58 · Answer 15 · 2026-03-26 04:29:20

58

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Cauchy's differentiation formula for bounded operators

Published on 26 Mar 2026 - 4:29

List Question

$f: D\to \mathbb C$ is holomorphic such that $diam f(D)=d$, then $|f'(0)|=d/2\implies f$ is linear.

Does the $\Gamma\subset\mathbb{C}$ curve always has to be smooth in Cauchy's integral theorem?

Cauchy integral formula for a unbounded domain

Upper bound of a function in Hoffman and Mardsten's Complex Analysis 2.8

How to prove that a sum is inclosed by two upper and lower bounds (values)?

Prove that if $f$ is holomorphic inside and on a circle of radius $R$ centered at $z_0$, then $|f(z_0)| \geq \min_{z \in C_{R}(z_0)} |f(z)|$

How to show $\mathbb E[f(X)]=f(\mu +i\sigma)$ using Cauchy integral formula

Show that integral $\int \frac{f'(w)}{w-z} dw = \int \frac{f(w)}{(w-z)^2} dw$

Example for complex integral

Choosing a path for reverse Cauchy integral formula

Complex conjugate by complex integration

Integrating $\frac {e^{-iz}}{z}$ over a semicircle counter-clockwise around $0$ of infinite radius $r$

Compute integrals using Cauchy Integral Formula

Can this given $f: S^1\to \mathbb C$ be extended to a continuous $F: \overline{\mathbb D}\to \mathbb C, F$ is holomorphic on $\mathbb D$?

Cauchy's differentiation formula for bounded operators

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