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From Donaldson's Riemann Surfaces- Existence of non-vanishing $C^\infty$ function $ f(t)= 1$ for small $t$, $f(t)=\frac{1}{t}$for large $t$

score 171 · Answer 1 · 2026-03-24 20:33:37

171

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From Donaldson's Riemann Surfaces- Existence of non-vanishing $C^\infty$ function $ f(t)= 1$ for small $t$, $f(t)=\frac{1}{t}$for large $t$

Published on 24 Mar 2026 - 20:33

score 1.1k · Answer 2 · 2026-04-06 20:06:14

1.1k

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Why is $\frac{df}{d\bar z}=0$ necessary if $f$ is an analytic function?

Published on 06 Apr 2026 - 20:06

score 91 · Answer 3 · 2026-04-09 01:40:50

91

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Find all values of following inverse hyperbolic trig function

Published on 09 Apr 2026 - 1:40

score 61 · Answer 4 · 2026-03-26 12:40:37

61

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Decide and prove whether the following functions are complex differentiable. If so, find their derivatives.

Published on 26 Mar 2026 - 12:40

score 36 · Answer 5 · 2018-02-13 23:08:35

36

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Zeros of Function from $\mathbb{R}^n$ to $\mathbb{C}$ - What's the shape?

Published on 13 Feb 2018 - 23:08

score 211 · Answer 6 · 2018-02-14 04:51:01

211

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Find the branch cut structure associated with the function

Published on 14 Feb 2018 - 4:51

score 24 · Answer 7 · 2018-02-14 04:55:28

24

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Show $\dfrac{g(z)-g(z_0)}{z-z_0}-f(z_0)\to 0$ as $z\to z_0$

Published on 14 Feb 2018 - 4:55

score 96 · Answer 8 · 2018-02-14 05:08:06

96

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Show that $\frac{1}{2\pi}\int_0^{2\pi} |f(re^{it})|^2\,dt=\sum\limits_{n=0}^\infty |a_n|^2 r^{2n}$

Published on 14 Feb 2018 - 5:08

score 7k · Answer 9 · 2026-04-12 07:21:15

7k

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Solve complex equation $z^3=1-i$

Published on 12 Apr 2026 - 7:21

score 209 · Answer 10 · 2026-04-09 02:07:17

209

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Published on 09 Apr 2026 - 2:07

score 749 · Answer 11 · 2026-03-26 19:05:17

749

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score 596 · Answer 12 · 2026-03-26 19:20:56

596

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Published on 26 Mar 2026 - 19:20

score 70 · Answer 13 · 2026-04-12 05:16:55

70

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Verification of $\lim_{n \to \infty} \frac{7n - i}{3n^2 - ni - 2 - i}$

Published on 12 Apr 2026 - 5:16

score 385 · Answer 14 · 2026-04-11 16:47:02

385

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On real roots of a polynomial equation

Published on 11 Apr 2026 - 16:47

score 201 · Answer 15 · 2026-04-11 16:11:03

201

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Argument Principle Application

Published on 11 Apr 2026 - 16:11

List Question

From Donaldson's Riemann Surfaces- Existence of non-vanishing $C^\infty$ function $ f(t)= 1$ for small $t$, $f(t)=\frac{1}{t}$for large $t$

Why is $\frac{df}{d\bar z}=0$ necessary if $f$ is an analytic function?

Find all values of following inverse hyperbolic trig function

Decide and prove whether the following functions are complex differentiable. If so, find their derivatives.

Zeros of Function from $\mathbb{R}^n$ to $\mathbb{C}$ - What's the shape?

Find the branch cut structure associated with the function

Show $\dfrac{g(z)-g(z_0)}{z-z_0}-f(z_0)\to 0$ as $z\to z_0$

Show that $\frac{1}{2\pi}\int_0^{2\pi} |f(re^{it})|^2\,dt=\sum\limits_{n=0}^\infty |a_n|^2 r^{2n}$

Solve complex equation $z^3=1-i$

Is $F$ continuous on the closed unit disk $D(0, 1)$?

Describing automorphisms of a punctured unit disc

What is the Taylor series of $\sqrt{z}$ around $z=-1$

Verification of $\lim_{n \to \infty} \frac{7n - i}{3n^2 - ni - 2 - i}$

On real roots of a polynomial equation

Argument Principle Application

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