Question

Prove by direct computation that $f^{[2]}(z) =\frac{1}{\pi i}\oint_{\partial D_1(0)} \frac{f(w)dw}{(w-z)^3} \text{ for } z \in D_1(0).$

score 34 · Answer 1 · 2026-04-15 20:13:19

34

Views

Prove by direct computation that $f^{[2]}(z) =\frac{1}{\pi i}\oint_{\partial D_1(0)} \frac{f(w)dw}{(w-z)^3} \text{ for } z \in D_1(0).$

Published on 15 Apr 2026 - 20:13

score 190 · Answer 2 · 2026-04-14 18:07:10

190

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Complex Analysis - Is the function f : $z → $ $\overline z $ $(1 + z^ 2 )$ complex differential on C?

Published on 14 Apr 2026 - 18:07

score 42 · Answer 3 · 2026-04-12 02:57:13

42

Views

Why does $f'(z)$ only involve partial derivatives on $x$ and not also on $y$?

Published on 12 Apr 2026 - 2:57

score 354 · Answer 4 · 2026-04-23 20:08:29

354

Views

Is it possible to say that $\arg(0)= \infty $ since it's not undefined or it is $0$ since $0|0$?

Published on 23 Apr 2026 - 20:08

score 83 · Answer 5 · 2026-04-12 16:56:40

83

Views

Calculate this integral using residues

Published on 12 Apr 2026 - 16:56

score 61 · Answer 6 · 2026-04-13 17:49:46

61

Views

Show that if $w$ is a zero of $P(z)$ (a complex polynomial) than $1/w$ is also

Published on 13 Apr 2026 - 17:49

score 75 · Answer 7 · 2026-03-25 01:18:39

75

Views

Image of $f(z)=\frac{z-3}{z-4}$ on $\{z\in\mathbb{C}|2<Re(z)<3\}$

Published on 25 Mar 2026 - 1:18

score 411 · Answer 8 · 2026-04-11 20:09:57

411

Views

How to integrate the complex function $f(z) = xy$ over the circle $C = [0, r]$

Published on 11 Apr 2026 - 20:09

score 69 · Answer 9 · 2026-04-14 19:10:12

69

Views

$f:D\to D$ is strictly contracting with respect to the hyperbolic metric

Published on 14 Apr 2026 - 19:10

score 100 · Answer 10 · 2026-03-25 09:27:10

100

Views

Infimum over a class of holomorphic functions on the unit disk

Published on 25 Mar 2026 - 9:27

score 205 · Answer 11 · 2026-04-09 22:59:58

205

Views

Complex function to its 2D equivalent

Published on 09 Apr 2026 - 22:59

score 216 · Answer 12 · 2026-04-15 03:20:50

216

Views

Prove that every zero of $z^{4}-5z+1$ has multiplicity 1

Published on 15 Apr 2026 - 3:20

score 2k · Answer 13 · 2026-04-13 16:05:44

2k

Views

Finding the residue of $\frac{\sinh z}{z^2 \cosh z}$ at $z= \pi i /2$

Published on 13 Apr 2026 - 16:05

score 134 · Answer 14 · 2026-04-15 08:51:31

134

Views

How are the sheets of $y^3 = x(x-1)(x+1)$ arranged?

Published on 15 Apr 2026 - 8:51

score 630 · Answer 15 · 2026-04-15 21:27:15

630

Views

Reflect the line $y=x$ in the circle $|z-2|=1$

Published on 15 Apr 2026 - 21:27

List Question

Prove by direct computation that $f^{[2]}(z) =\frac{1}{\pi i}\oint_{\partial D_1(0)} \frac{f(w)dw}{(w-z)^3} \text{ for } z \in D_1(0).$

Complex Analysis - Is the function f : $z → $ $\overline z $ $(1 + z^ 2 )$ complex differential on C?

Why does $f'(z)$ only involve partial derivatives on $x$ and not also on $y$?

Is it possible to say that $\arg(0)= \infty $ since it's not undefined or it is $0$ since $0|0$?

Calculate this integral using residues

Show that if $w$ is a zero of $P(z)$ (a complex polynomial) than $1/w$ is also

Image of $f(z)=\frac{z-3}{z-4}$ on $\{z\in\mathbb{C}|2<Re(z)<3\}$

How to integrate the complex function $f(z) = xy$ over the circle $C = [0, r]$

$f:D\to D$ is strictly contracting with respect to the hyperbolic metric

Infimum over a class of holomorphic functions on the unit disk

Complex function to its 2D equivalent

Prove that every zero of $z^{4}-5z+1$ has multiplicity 1

Finding the residue of $\frac{\sinh z}{z^2 \cosh z}$ at $z= \pi i /2$

How are the sheets of $y^3 = x(x-1)(x+1)$ arranged?

Reflect the line $y=x$ in the circle $|z-2|=1$

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