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holomorphic function from punctured disc that misses a slit has an essential singularity at the hole

score 507 · Answer 1 · 2026-04-14 05:02:51

507

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holomorphic function from punctured disc that misses a slit has an essential singularity at the hole

Published on 14 Apr 2026 - 5:02

score 72 · Answer 2 · 2026-04-24 03:47:04

72

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Is $\log|f|$ continuous or just upper semicontinuous?

Published on 24 Apr 2026 - 3:47

score 48 · Answer 3 · 2026-04-14 10:17:07

48

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holomorphic function from the unit disc to itself with special point implies bound on $|f(0)|$

Published on 14 Apr 2026 - 10:17

score 177 · Answer 4 · 2026-04-16 03:55:43

Let $f$ be holomorphic with zeros at $\frac{1}{2}$ and $\frac{-1}{2}$ such that $|f(z)| < 1$ on $D$. Show $|f(i/2)| \leq \frac{8}{17}$.

score 49 · Answer 5 · 2026-04-16 05:53:52

49

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Let $f$ be a monic polynomial such that $\lvert f \rvert \leq 1$ if $ \lvert z \rvert \leq 1$, then $f = z^n$.

Published on 16 Apr 2026 - 5:53

score 3.5k · Answer 6 · 2026-04-10 09:08:20

3.5k

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what is $e^{ix}$ as $x \to \infty$

Published on 10 Apr 2026 - 9:08

score 82 · Answer 7 · 2026-04-10 22:49:02

82

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Complex Analysis: Complex Integral

Published on 10 Apr 2026 - 22:49

score 30 · Answer 8 · 2026-04-11 06:08:19

30

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How to prove the following result for complex vectors?

Published on 11 Apr 2026 - 6:08

score 193 · Answer 9 · 2026-04-16 13:01:41

193

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If $f(z)$ and $g(z)$ are not analytic, then $fg$ can be analytic?

Published on 16 Apr 2026 - 13:01

score 36 · Answer 10 · 2026-04-14 00:11:19

36

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A function with $R_0(f)=\sum_{n\ge0} \frac{1}{n!(n+1)!}$

Published on 14 Apr 2026 - 0:11

score 145 · Answer 11 · 2026-04-11 13:05:20

145

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Proof: $f(z)$ is constant

Published on 11 Apr 2026 - 13:05

score 196 · Answer 12 · 2026-04-22 21:39:40

196

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Compactification of $\mathbb{C}$ and complex curves

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score 60 · Answer 13 · 2026-04-11 03:22:14

60

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score 415 · Answer 14 · 2026-04-10 19:49:21

415

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Proof: complex exponential inequality

Published on 10 Apr 2026 - 19:49

score 358 · Answer 15 · 2026-03-25 03:24:16

358

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Characteristic function and convergence in distribution

Published on 25 Mar 2026 - 3:24

List Question

holomorphic function from punctured disc that misses a slit has an essential singularity at the hole

Is $\log|f|$ continuous or just upper semicontinuous?

holomorphic function from the unit disc to itself with special point implies bound on $|f(0)|$

Let $f$ be holomorphic with zeros at $\frac{1}{2}$ and $\frac{-1}{2}$ such that $|f(z)| < 1$ on $D$. Show $|f(i/2)| \leq \frac{8}{17}$.

Let $f$ be a monic polynomial such that $\lvert f \rvert \leq 1$ if $ \lvert z \rvert \leq 1$, then $f = z^n$.

what is $e^{ix}$ as $x \to \infty$

Complex Analysis: Complex Integral

How to prove the following result for complex vectors?

If $f(z)$ and $g(z)$ are not analytic, then $fg$ can be analytic?

A function with $R_0(f)=\sum_{n\ge0} \frac{1}{n!(n+1)!}$

Proof: $f(z)$ is constant

Compactification of $\mathbb{C}$ and complex curves

Cauchy's formula - evaluating complex integrals

Proof: complex exponential inequality

Characteristic function and convergence in distribution

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