Question

Singularities of $f(z) = \frac{z^2}{\cos(z) - 1}$

score 71 · Answer 1 · 2018-02-19 17:34:42

71

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Singularities of $f(z) = \frac{z^2}{\cos(z) - 1}$

Published on 19 Feb 2018 - 17:34

score 56 · Answer 2 · 2026-03-26 14:23:04

56

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Parametrisation of the boundary of the image of $f(z) = e^z$

Published on 26 Mar 2026 - 14:23

score 485 · Answer 3 · 2026-04-09 00:30:00

485

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Bose-Einstein function as real part of polylogarithm: $\overline{G}_{s}(x)= \Re \mathrm{Li}_{s+1}(e^x)$

Published on 09 Apr 2026 - 0:30

score 694 · Answer 4 · 2026-04-08 22:44:37

694

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branch cut and branch points for $f(z)=[(z-1)(z-2)]^{1/3}$

Published on 08 Apr 2026 - 22:44

score 880 · Answer 5 · 2026-04-11 22:27:03

880

Views

Integrating a function over a vertical line in the complex plane

Published on 11 Apr 2026 - 22:27

score 173 · Answer 6 · 2026-03-26 14:20:53

173

Views

Let $z = 5e^{2πi/3}$ . Find the smallest positive integer n such that $(zi)^n ∈ \mathbb{Q}$

Published on 26 Mar 2026 - 14:20

score 38 · Answer 7 · 2026-04-10 17:29:31

38

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What does it mean to find a location of a singularity?

Published on 10 Apr 2026 - 17:29

score 267 · Answer 8 · 2026-04-06 16:27:13

267

Views

Square Contour Show that $|\sin(z)| \ge \sinh(\pi/2)$

Published on 06 Apr 2026 - 16:27

score 57 · Answer 9 · 2018-02-20 00:16:46

57

Views

Show that $\sum_{n=1}^{\infty}\frac{1}{n^z}$ converges locally uniformly on the set $\textrm{Re}(z) > 1$

Published on 20 Feb 2018 - 0:16

score 132 · Answer 10 · 2026-03-25 07:44:52

132

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Upper Bounds on Contour Integral $\frac{1}{Length(C)}\ \left| \int_{C}zdz\right| \le 2^{-1/6}$

Published on 25 Mar 2026 - 7:44

score 570 · Answer 11 · 2026-04-07 08:18:10

570

Views

Map the outside of the parabola $y^2 = 2px$ on the disc $|w|<1$ such that $z=0$ and $z=-\frac{p}{2}$ are mapped to $w=1$ and $w=0$

Published on 07 Apr 2026 - 8:18

score 332 · Answer 12 · 2018-02-20 05:11:01

332

Views

Branch cuts without intersection

Published on 20 Feb 2018 - 5:11

score 40 · Answer 13 · 2026-04-02 18:27:13

40

Views

Is $\|e^{zT-zT^*}\|$ bounded for all $z\in \mathbb{C}$?

Published on 02 Apr 2026 - 18:27

score 201 · Answer 14 · 2026-04-09 16:02:26

201

Views

Is this definition of a function wrong?

Published on 09 Apr 2026 - 16:02

score 97 · Answer 15 · 2026-04-11 12:56:30

97

Views

How do I solve this trivial complex integral $\int^w_0 \frac{bz}{(z-a)(z+a)}\textrm{d}z$?

Published on 11 Apr 2026 - 12:56

List Question

Singularities of $f(z) = \frac{z^2}{\cos(z) - 1}$

Parametrisation of the boundary of the image of $f(z) = e^z$

Bose-Einstein function as real part of polylogarithm: $\overline{G}_{s}(x)= \Re \mathrm{Li}_{s+1}(e^x)$

branch cut and branch points for $f(z)=[(z-1)(z-2)]^{1/3}$

Integrating a function over a vertical line in the complex plane

Let $z = 5e^{2πi/3}$ . Find the smallest positive integer n such that $(zi)^n ∈ \mathbb{Q}$

What does it mean to find a location of a singularity?

Square Contour Show that $|\sin(z)| \ge \sinh(\pi/2)$

Show that $\sum_{n=1}^{\infty}\frac{1}{n^z}$ converges locally uniformly on the set $\textrm{Re}(z) > 1$

Upper Bounds on Contour Integral $\frac{1}{Length(C)}\ \left| \int_{C}zdz\right| \le 2^{-1/6}$

Map the outside of the parabola $y^2 = 2px$ on the disc $|w|<1$ such that $z=0$ and $z=-\frac{p}{2}$ are mapped to $w=1$ and $w=0$

Branch cuts without intersection

Is $\|e^{zT-zT^*}\|$ bounded for all $z\in \mathbb{C}$?

Is this definition of a function wrong?

How do I solve this trivial complex integral $\int^w_0 \frac{bz}{(z-a)(z+a)}\textrm{d}z$?

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