Question

Complex Analysis 2.1.2 - 1 If g(w) and f(z) are analytic functions, show that g(f(z)) is also analytic.

score 701 · Answer 1 · 2026-03-25 22:30:44

701

Views

Complex Analysis 2.1.2 - 1 If g(w) and f(z) are analytic functions, show that g(f(z)) is also analytic.

Published on 25 Mar 2026 - 22:30

score 45 · Answer 2 · 2026-03-25 03:04:32

45

Views

Suppose that for $\theta \in R$ we have $f(z)=g(z,\theta)$. Now fix $z=z_0$, is $g(z_0,\theta)=f(z_0)$ for all $\theta$ in its domain?

Published on 25 Mar 2026 - 3:04

score 188 · Answer 3 · 2026-03-25 18:24:40

188

Views

Analytic functions having non-zero derivative preserve angle between two curves.

Published on 25 Mar 2026 - 18:24

score 74 · Answer 4 · 2020-01-09 07:50:19

74

Views

Does there exist a non-open connected set where the derivative of $f$ vanishes without $f$ being constant?

Published on 09 Jan 2020 - 7:50

score 44 · Answer 5 · 2026-03-25 21:01:20

44

Views

Conformal map from a 7-sided polyhedron to a square pyramid.

Published on 25 Mar 2026 - 21:01

score 1.2k · Answer 6 · 2020-01-14 07:51:46

1.2k

Views

If $f(z)$ is analytic, and $\overline{f(z)}$ is analytic, then is $f$ necessarily a constant function?

Published on 14 Jan 2020 - 7:51

score 279 · Answer 7 · 2020-01-15 14:23:15

279

Views

Application of Riemann Mapping Theorem to prove uniqueness

Published on 15 Jan 2020 - 14:23

score 65 · Answer 8 · 2020-01-16 17:32:20

65

Views

Does there exist analytic functions satisfying the following property?

Published on 16 Jan 2020 - 17:32

score 158 · Answer 9 · 2020-01-17 01:13:57

158

Views

If an asymptotic expansion is valid as $\text{Re}(z)\to\infty$, must it be valid as $\text{Im}(z)\to\infty$?

Published on 17 Jan 2020 - 1:13

score 363 · Answer 10 · 2026-03-25 22:25:58

363

Views

Proof that $H(z)=\int_0^\infty h(z,t)\,dt$ is analytic?

Published on 25 Mar 2026 - 22:25

score 234 · Answer 11 · 2020-01-21 18:25:39

234

Views

Real, analytic exponential factorial $f(x) = x^{f(x-1)}$

Published on 21 Jan 2020 - 18:25

score 62 · Answer 12 · 2026-03-25 22:11:26

62

Views

Strong Maximum Principle: every sequence $z_n\in U$ converging to $\partial U$ or $|z_n|\to\infty$

Published on 25 Mar 2026 - 22:11

score 128 · Answer 13 · 2020-01-23 13:59:30

128

Views

Find number of solutions of $x = a\sin x$

Published on 23 Jan 2020 - 13:59

score 92 · Answer 14 · 2026-03-25 18:56:29

92

Views

Given a Möbius Transformation $w=f(z)$ find $f(-\bar{z})$

Published on 25 Mar 2026 - 18:56

score 28 · Answer 15 · 2020-02-01 18:45:09

28

Views

Is a complex function analytic on a domain $D$ if $D$ contains an isolated singularity?

Published on 01 Feb 2020 - 18:45

List Question

Complex Analysis 2.1.2 - 1 If g(w) and f(z) are analytic functions, show that g(f(z)) is also analytic.

Suppose that for $\theta \in R$ we have $f(z)=g(z,\theta)$. Now fix $z=z_0$, is $g(z_0,\theta)=f(z_0)$ for all $\theta$ in its domain?

Analytic functions having non-zero derivative preserve angle between two curves.

Does there exist a non-open connected set where the derivative of $f$ vanishes without $f$ being constant?

Conformal map from a 7-sided polyhedron to a square pyramid.

If $f(z)$ is analytic, and $\overline{f(z)}$ is analytic, then is $f$ necessarily a constant function?

Application of Riemann Mapping Theorem to prove uniqueness

Does there exist analytic functions satisfying the following property?

If an asymptotic expansion is valid as $\text{Re}(z)\to\infty$, must it be valid as $\text{Im}(z)\to\infty$?

Proof that $H(z)=\int_0^\infty h(z,t)\,dt$ is analytic?

Real, analytic exponential factorial $f(x) = x^{f(x-1)}$

Strong Maximum Principle: every sequence $z_n\in U$ converging to $\partial U$ or $|z_n|\to\infty$

Find number of solutions of $x = a\sin x$

Given a Möbius Transformation $w=f(z)$ find $f(-\bar{z})$

Is a complex function analytic on a domain $D$ if $D$ contains an isolated singularity?

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