Question

Prove that there is holomorphic function $f:G \rightarrow \mathbb{C}$ with $e^{f(z)}=z$

score 521 · Answer 1 · 2026-04-15 12:37:22

521

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Prove that there is holomorphic function $f:G \rightarrow \mathbb{C}$ with $e^{f(z)}=z$

Published on 15 Apr 2026 - 12:37

score 51 · Answer 2 · 2026-04-15 14:28:59

51

Views

Rational functions and residues

Published on 15 Apr 2026 - 14:28

score 429 · Answer 3 · 2026-04-10 11:23:47

429

Views

Construction a harmonic function

Published on 10 Apr 2026 - 11:23

score 339 · Answer 4 · 2026-04-14 05:13:33

339

Views

If $\sum a_n$ and $\sum b_n$ and their convolution $\sum c_n$ converge, then $\sum c_n=\sum a_n\sum b_n$

Published on 14 Apr 2026 - 5:13

score 2.3k · Answer 5 · 2026-04-15 06:04:39

Show that the mapping $w=z+\frac1z$ maps the domain outside the circle $|z| = 1$ onto the rest of the $w$ plane.

score 1.9k · Answer 6 · 2026-04-14 22:37:35

1.9k

Views

If $z_1+z_2+z_3=0$ and $|z_1|=|z_2|=|z_3|=1$, then $z_1,z_2,z_3$ are the vertices of an equilateral triangle.

Published on 14 Apr 2026 - 22:37

score 236 · Answer 7 · 2026-04-14 10:47:22

236

Views

extending convergence radius using one boundary point

Published on 14 Apr 2026 - 10:47

score 341 · Answer 8 · 2026-04-12 22:29:52

341

Views

Is connectedness required to show that an analytic function with no zeros in a compact set but constant modulus on the boundary is constant?

Published on 12 Apr 2026 - 22:29

score 187 · Answer 9 · 2026-04-14 17:00:24

187

Views

If $h$ is an arbitrary holomorphic function then there exist $\phi_1, \phi_2$ holomorphic such that $h = f\phi_1 + g\phi_2$

Published on 14 Apr 2026 - 17:00

score 79 · Answer 10 · 2026-04-12 14:56:12

79

Views

Tell whether module of root of such polynomial is smaller than 1

Published on 12 Apr 2026 - 14:56

score 580 · Answer 11 · 2026-04-08 23:37:28

580

Views

Checking whether a complex function has an antiderivative

Published on 08 Apr 2026 - 23:37

score 1.2k · Answer 12 · 2026-04-15 08:17:46

Show that when a circle is transformed into a circle under $w = 1/z $ the center is never mapped onto the center of the image circle.

score 411 · Answer 13 · 2026-04-11 15:27:23

411

Views

null-homotopic $\Leftrightarrow$ free-null-homotopic

Published on 11 Apr 2026 - 15:27

score 326 · Answer 14 · 2026-04-29 12:25:10

326

Views

Question concerning Schwarz-Christoffel Mappings and Conformal Modulus

Published on 29 Apr 2026 - 12:25

score 155 · Answer 15 · 2026-03-24 20:38:03

155

Views

Rouche's Theorem of functions other than polynomial

Published on 24 Mar 2026 - 20:38

List Question

Prove that there is holomorphic function $f:G \rightarrow \mathbb{C}$ with $e^{f(z)}=z$

Rational functions and residues

Construction a harmonic function

If $\sum a_n$ and $\sum b_n$ and their convolution $\sum c_n$ converge, then $\sum c_n=\sum a_n\sum b_n$

Show that the mapping $w=z+\frac1z$ maps the domain outside the circle $|z| = 1$ onto the rest of the $w$ plane.

If $z_1+z_2+z_3=0$ and $|z_1|=|z_2|=|z_3|=1$, then $z_1,z_2,z_3$ are the vertices of an equilateral triangle.

extending convergence radius using one boundary point

Is connectedness required to show that an analytic function with no zeros in a compact set but constant modulus on the boundary is constant?

If $h$ is an arbitrary holomorphic function then there exist $\phi_1, \phi_2$ holomorphic such that $h = f\phi_1 + g\phi_2$

Tell whether module of root of such polynomial is smaller than 1

Checking whether a complex function has an antiderivative

Show that when a circle is transformed into a circle under $w = 1/z $ the center is never mapped onto the center of the image circle.

null-homotopic $\Leftrightarrow$ free-null-homotopic

Question concerning Schwarz-Christoffel Mappings and Conformal Modulus

Rouche's Theorem of functions other than polynomial

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