Question

Roots of a complex number, solutions

score 38 · Answer 1 · 2026-04-11 19:29:09

38

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Roots of a complex number, solutions

Published on 11 Apr 2026 - 19:29

score 78 · Answer 2 · 2026-04-12 04:28:41

78

Views

A conjecture on bounded complex partial sums

Published on 12 Apr 2026 - 4:28

score 75 · Answer 3 · 2026-04-13 22:48:29

75

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Why does the pole of $\frac{1-e^{2z}}{z^3}$ have order $2$?

Published on 13 Apr 2026 - 22:48

score 534 · Answer 4 · 2026-04-14 23:33:59

534

Views

The image of the line $\operatorname{Re}(z) = 1$ under $f(z) = (1+i)\frac1z - 2i$

Published on 14 Apr 2026 - 23:33

score 811 · Answer 5 · 2026-04-15 19:14:47

Let $f$ be entire. Assume that the function $g(z) = f(z)f(\frac{1}{z})$ is bounded on $\mathbb{C}-\{0\}$. Show that $f(z)=cz^m$

score 57 · Answer 6 · 2026-04-09 22:18:52

57

Views

What is a faithful representation of a Riemann surface?

Published on 09 Apr 2026 - 22:18

score 74 · Answer 7 · 2026-03-25 07:44:39

74

Views

Showing that $\sum\limits_{l=0}^\infty \frac{1}{(3l+2)!}=\frac{1}{3}(e-\frac{2}{\sqrt{e}} \cos(\frac{\pi}{3}-\frac{\sqrt{3}}{2}))$

Published on 25 Mar 2026 - 7:44

score 375 · Answer 8 · 2026-03-28 02:40:20

375

Views

Irreducible point in a complex (analytic) space

Published on 28 Mar 2026 - 2:40

score 295 · Answer 9 · 2026-03-25 07:45:35

295

Views

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Published on 25 Mar 2026 - 7:45

score 55 · Answer 10 · 2026-03-25 09:38:04

55

Views

Show that $\varphi_X(2\pi k)=\operatorname E(e^{i2\pi kX})=1 $

Published on 25 Mar 2026 - 9:38

score 49 · Answer 11 · 2026-04-10 23:33:47

49

Views

Complex function series.

Published on 10 Apr 2026 - 23:33

score 487 · Answer 12 · 2026-04-10 00:25:48

487

Views

If two positively oriented bases define the same lattice, then there is a matrix in $\operatorname{SL}(2,\mathbb{Z})$ acting on this basis

Published on 10 Apr 2026 - 0:25

score 61 · Answer 13 · 2026-04-17 14:19:28

61

Views

Laurent Series of $\frac{e^z}{z(1+z^2)}$ [at z=0]

Published on 17 Apr 2026 - 14:19

score 2.8k · Answer 14 · 2026-04-29 12:43:44

2.8k

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If $|z| < 1$, prove that $\Re \left(\frac{1}{1 - z} \right) > \frac{1}{2}$.

Published on 29 Apr 2026 - 12:43

score 68 · Answer 15 · 2026-04-15 08:37:11

68

Views

Prove that $f$ is differentiable in a whole $\mathbb{C}$ set.

Published on 15 Apr 2026 - 8:37

List Question

Roots of a complex number, solutions

A conjecture on bounded complex partial sums

Why does the pole of $\frac{1-e^{2z}}{z^3}$ have order $2$?

The image of the line $\operatorname{Re}(z) = 1$ under $f(z) = (1+i)\frac1z - 2i$

Let $f$ be entire. Assume that the function $g(z) = f(z)f(\frac{1}{z})$ is bounded on $\mathbb{C}-\{0\}$. Show that $f(z)=cz^m$

What is a faithful representation of a Riemann surface?

Showing that $\sum\limits_{l=0}^\infty \frac{1}{(3l+2)!}=\frac{1}{3}(e-\frac{2}{\sqrt{e}} \cos(\frac{\pi}{3}-\frac{\sqrt{3}}{2}))$

Irreducible point in a complex (analytic) space

Show that $\sum\limits_{n=0}^{\infty} \binom{3n}{n} (\frac{4}{125})^n=\frac{1}{2\pi i}\int_{C(0;1)}\frac{-125}{(z-4)(4z^2+28z-1)}dz$

Show that $\varphi_X(2\pi k)=\operatorname E(e^{i2\pi kX})=1 $

Complex function series.

If two positively oriented bases define the same lattice, then there is a matrix in $\operatorname{SL}(2,\mathbb{Z})$ acting on this basis

Laurent Series of $\frac{e^z}{z(1+z^2)}$ [at z=0]

If $|z| < 1$, prove that $\Re \left(\frac{1}{1 - z} \right) > \frac{1}{2}$.

Prove that $f$ is differentiable in a whole $\mathbb{C}$ set.

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