Question

What does $\int dz \,d\bar z\,\partial_z \,f(z,\bar z)$ evaluate to?

score 1.4k · Answer 1 · 2026-04-12 15:57:14

1.4k

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What does $\int dz \,d\bar z\,\partial_z \,f(z,\bar z)$ evaluate to?

Published on 12 Apr 2026 - 15:57

score 133 · Answer 2 · 2026-04-13 18:46:01

133

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Showing $\frac{1}{z}$ cannot be approximated by any polynomial on $\partial{\mathbb{D}}$.

Published on 13 Apr 2026 - 18:46

score 106 · Answer 3 · 2026-04-18 18:02:04

106

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Where does the following formula come from?

Published on 18 Apr 2026 - 18:02

score 595 · Answer 4 · 2026-04-16 10:27:39

595

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Evaluate $\int_{\left | z \right |=3} (e^{z}-1)dz/(z(z-1)(z-i))$

Published on 16 Apr 2026 - 10:27

score 48 · Answer 5 · 2026-03-25 04:43:04

48

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Need help with $\frac{w-a}{1-\overline{a}w} = \mu\frac{z-a}{1-\overline{a}z}$

Published on 25 Mar 2026 - 4:43

score 126 · Answer 6 · 2026-04-16 03:29:40

126

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An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$

Published on 16 Apr 2026 - 3:29

score 114 · Answer 7 · 2026-04-28 02:24:09

114

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combinatorics for valid Password with blacklist word

Published on 28 Apr 2026 - 2:24

score 10.5k · Answer 8 · 2026-04-30 13:18:11

10.5k

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Poles of $\sin(1/z)$

Published on 30 Apr 2026 - 13:18

score 262 · Answer 9 · 2026-04-16 15:52:41

262

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If $f(z)$ is entire function such that $|f(z)f'(z)| \leq 1$ then $f(z)$ is constant

Published on 16 Apr 2026 - 15:52

score 67 · Answer 10 · 2026-04-15 00:12:41

67

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$w \mapsto \frac{1}{2i\pi} \int_{\gamma}\frac{1}{z-w}\mathrm{d}z$ from $\mathbb{C} \setminus \gamma([a,b]) \to \mathbb{C}$ is continuous

Published on 15 Apr 2026 - 0:12

score 194 · Answer 11 · 2026-04-12 18:04:45

194

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Let $f$ be holomorphic in $\mathbb{C}\setminus\{i,2i\}$.

Published on 12 Apr 2026 - 18:04

score 55 · Answer 12 · 2026-03-26 02:20:45

55

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Finding the cauchy integral for $I(n)=\int_\gamma \frac{\cos{z}}{(z-z_0)^3}{dz}$ when $\gamma: |z|=3.$

Published on 26 Mar 2026 - 2:20

score 88 · Answer 13 · 2026-04-09 01:33:49

88

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How to derive this integral identity?

Published on 09 Apr 2026 - 1:33

score 341 · Answer 14 · 2026-04-14 16:55:55

341

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Asymptotic behavior of trigonometric functions near infinity

Published on 14 Apr 2026 - 16:55

score 411 · Answer 15 · 2026-05-04 03:55:58

411

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Do any authors take the sheaf-theoretic viewpoint on multivalued functions and/or indefinite integrals?

Published on 04 May 2026 - 3:55

List Question

What does $\int dz \,d\bar z\,\partial_z \,f(z,\bar z)$ evaluate to?

Showing $\frac{1}{z}$ cannot be approximated by any polynomial on $\partial{\mathbb{D}}$.

Where does the following formula come from?

Evaluate $\int_{\left | z \right |=3} (e^{z}-1)dz/(z(z-1)(z-i))$

Need help with $\frac{w-a}{1-\overline{a}w} = \mu\frac{z-a}{1-\overline{a}z}$

An analytic function $f$ on $\{z \in\mathbb{C} : |z|>1 \}$

combinatorics for valid Password with blacklist word

Poles of $\sin(1/z)$

If $f(z)$ is entire function such that $|f(z)f'(z)| \leq 1$ then $f(z)$ is constant

$w \mapsto \frac{1}{2i\pi} \int_{\gamma}\frac{1}{z-w}\mathrm{d}z$ from $\mathbb{C} \setminus \gamma([a,b]) \to \mathbb{C}$ is continuous

Let $f$ be holomorphic in $\mathbb{C}\setminus\{i,2i\}$.

Finding the cauchy integral for $I(n)=\int_\gamma \frac{\cos{z}}{(z-z_0)^3}{dz}$ when $\gamma: |z|=3.$

How to derive this integral identity?

Asymptotic behavior of trigonometric functions near infinity

Do any authors take the sheaf-theoretic viewpoint on multivalued functions and/or indefinite integrals?

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