Question

Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.

score 1.8k · Answer 1 · 2026-03-25 16:03:01

1.8k

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Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.

Published on 25 Mar 2026 - 16:03

score 838 · Answer 2 · 2026-03-25 07:46:31

838

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Use maximum modules principle to prove that if $\sup_{|z| = R}|f(z)|\leq AR^{k} + B$ with $f$ entire, then $f$ is a polynomial

Published on 25 Mar 2026 - 7:46

score 42 · Answer 3 · 2026-03-25 01:34:50

42

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Biholomorphic functions and delaunay triangulation

Published on 25 Mar 2026 - 1:34

score 209 · Answer 4 · 2026-03-25 04:37:55

209

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Existance of an analytic function on unit disc

Published on 25 Mar 2026 - 4:37

score 62 · Answer 5 · 2026-03-25 07:46:20

62

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Why is $ I = \int_\Omega \frac{1}{z-\zeta}\Delta u(\zeta) d\zeta = -2i \int_{\partial \Omega} \frac{1}{z-\zeta}\partial u(\zeta) d\zeta. $?

Published on 25 Mar 2026 - 7:46

score 91 · Answer 6 · 2018-11-15 10:48:45

91

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Show existence of holomorphic function $h$ such that $e^{h(z)}=1+z^5+z^{10}$

Published on 15 Nov 2018 - 10:48

score 116 · Answer 7 · 2026-03-25 07:48:58

116

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holomorphic functions, roots of unity and harmonic numbers

Published on 25 Mar 2026 - 7:48

score 988 · Answer 8 · 2026-03-25 01:23:52

988

Views

Is the Lambert W function analytic? If not everywhere then on what set is it analytic?

Published on 25 Mar 2026 - 1:23

score 546 · Answer 9 · 2018-11-20 14:13:39

546

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Show that $\sum_{r=1}^\infty \frac{1}{(r-z)^2}$ is holomorphic on $\mathbb{C}\backslash\mathbb{N}$

Published on 20 Nov 2018 - 14:13

score 747 · Answer 10 · 2018-11-22 13:06:08

747

Views

Why is it called a holomorphic function?

Published on 22 Nov 2018 - 13:06

score 98 · Answer 11 · 2026-03-25 13:57:04

98

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$f$ is an entire function s.t $|f(z)|=1$ $\forall z \in \Bbb R$. prove that $f$ has no zeros in $\Bbb C$

Published on 25 Mar 2026 - 13:57

score 84 · Answer 12 · 2018-11-24 16:50:14

84

Views

Finding the residues of $\frac{\cos z -1}{(e^z-1)^2}$.

Published on 24 Nov 2018 - 16:50

score 41 · Answer 13 · 2018-11-26 09:45:22

41

Views

Complex Analytic Function's Power Series

Published on 26 Nov 2018 - 9:45

score 60 · Answer 14 · 2018-11-28 22:35:46

60

Views

Find all holomorphic functions that satisfy a condition

Published on 28 Nov 2018 - 22:35

score 366 · Answer 15 · 2026-03-25 06:02:29

366

Views

Holomorphic functions reflected through segments that aren't on the real axis

Published on 25 Mar 2026 - 6:02

List Question

Finding all differentiable $f(z) = u(x) + iv(y)$ in $\mathbb{C}$ where $u(x),v(y)$ are real valued functions.

Use maximum modules principle to prove that if $\sup_{|z| = R}|f(z)|\leq AR^{k} + B$ with $f$ entire, then $f$ is a polynomial

Biholomorphic functions and delaunay triangulation

Existance of an analytic function on unit disc

Why is $ I = \int_\Omega \frac{1}{z-\zeta}\Delta u(\zeta) d\zeta = -2i \int_{\partial \Omega} \frac{1}{z-\zeta}\partial u(\zeta) d\zeta. $?

Show existence of holomorphic function $h$ such that $e^{h(z)}=1+z^5+z^{10}$

holomorphic functions, roots of unity and harmonic numbers

Is the Lambert W function analytic? If not everywhere then on what set is it analytic?

Show that $\sum_{r=1}^\infty \frac{1}{(r-z)^2}$ is holomorphic on $\mathbb{C}\backslash\mathbb{N}$

Why is it called a holomorphic function?

$f$ is an entire function s.t $|f(z)|=1$ $\forall z \in \Bbb R$. prove that $f$ has no zeros in $\Bbb C$

Finding the residues of $\frac{\cos z -1}{(e^z-1)^2}$.

Complex Analytic Function's Power Series

Find all holomorphic functions that satisfy a condition

Holomorphic functions reflected through segments that aren't on the real axis

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