Question

Is $f(z) = |z|$ holomorphic on $\mathbb{C}$?

score 969 · Answer 1 · 2026-03-25 09:25:20

Is $f(z) = |z|$ holomorphic on $\mathbb{C}$?

Published on 25 Mar 2026 - 9:25

score 213 · Answer 2 · 2026-04-15 19:44:57

If $f$ is entire and for some $r>0$ we have $f(z)=Cz^n$ for a constant $C \in\mathbb C$ on $|z|=r$ then does it follow that $f(z)=Cz^n$ for all $z$?

score 38 · Answer 3 · 2026-04-11 08:48:21

38

Views

Calculating a complex line integral

Published on 11 Apr 2026 - 8:48

score 99 · Answer 4 · 2026-04-18 14:05:36

99

Views

Example of a unit circle subset that is $F_{\sigma\delta}$ but not $F_\sigma$

Published on 18 Apr 2026 - 14:05

score 270 · Answer 5 · 2026-04-12 11:55:57

270

Views

When is the image of a convex set under a holomorphic function convex?

Published on 12 Apr 2026 - 11:55

score 28 · Answer 6 · 2026-04-15 20:59:31

28

Views

How to prove that ||$\frac1{（4πit)^{n/2}}\int_{R^n}e^{i|x-y|^{2}/|4t}g(y)||L^2(R^n)$ is invariant with respect to time

Published on 15 Apr 2026 - 20:59

score 108 · Answer 7 · 2026-04-16 07:22:16

108

Views

f is holomorphic; if g(z) = $\pi$f(z)cot($\pi$z) show that $res_{z=z_0}$g(z) = f(n) for each n $\in$ $\Bbb Z$

Published on 16 Apr 2026 - 7:22

score 122 · Answer 8 · 2026-04-14 11:29:52

Show that if the origin is neither an essential singularity, nor a pole of order 2 or higher, then f must be constant

score 132 · Answer 9 · 2026-04-14 11:21:01

132

Views

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score 37 · Answer 10 · 2026-04-15 15:13:22

37

Views

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score 67 · Answer 11 · 2026-04-17 05:30:39

67

Views

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Published on 17 Apr 2026 - 5:30

score 105 · Answer 12 · 2026-04-13 17:44:38

105

Views

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Published on 13 Apr 2026 - 17:44

score 145 · Answer 13 · 2026-04-09 20:36:41

145

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Published on 09 Apr 2026 - 20:36

score 86 · Answer 14 · 2026-04-14 19:04:08

86

Views

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Published on 14 Apr 2026 - 19:04

score 584 · Answer 15 · 2026-04-15 08:21:39

584

Views

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Published on 15 Apr 2026 - 8:21

List Question

Is $f(z) = |z|$ holomorphic on $\mathbb{C}$?

If $f$ is entire and for some $r>0$ we have $f(z)=Cz^n$ for a constant $C \in\mathbb C$ on $|z|=r$ then does it follow that $f(z)=Cz^n$ for all $z$?

Calculating a complex line integral

Example of a unit circle subset that is $F_{\sigma\delta}$ but not $F_\sigma$

When is the image of a convex set under a holomorphic function convex?

How to prove that ||$\frac1{（4πit)^{n/2}}\int_{R^n}e^{i|x-y|^{2}/|4t}g(y)||L^2(R^n)$ is invariant with respect to time

f is holomorphic; if g(z) = $\pi$f(z)cot($\pi$z) show that $res_{z=z_0}$g(z) = f(n) for each n $\in$ $\Bbb Z$

Show that if the origin is neither an essential singularity, nor a pole of order 2 or higher, then f must be constant

Residue Theorem and Improper Integral

Prove that the following is an open set.

Express entire functions $f(z)$ by exact formula

Sequence of functions converges normally to $e^z$

Largest open set for analytic function

Interior of the line segment in the complex plane

Power series in $\mathbb{R}$ and $\mathbb{C}$

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