Question

Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer?

score 530 · Answer 1 · 2016-05-11 17:35:17

Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer?

Published on 11 May 2016 - 17:35

score 2.5k · Answer 2 · 2016-05-11 20:22:29

Suppose that for each $a\in \mathbb{C}$ at least one coefficient of the Taylor's series $f$ about $a$ is zero. Show that $f$ is a polynomial.

score 480 · Answer 3 · 2016-05-13 02:14:15

480

Views

Basic contour integral with Cauchy's Residue Theorem

Published on 13 May 2016 - 2:14

score 83 · Answer 4 · 2016-05-13 13:04:23

83

Views

The value of the integral $\int_{C} \dfrac{z^2+1 dz}{(z+1)(z+2)}$ where $C$ is $|z|=\dfrac{3}{2}$

Published on 13 May 2016 - 13:04

score 214 · Answer 5 · 2026-04-01 03:58:24

214

Views

Choice of branch cut

Published on 01 Apr 2026 - 3:58

score 587 · Answer 6 · 2016-05-14 03:03:30

587

Views

Closed contour integral: $\int_{\mathbb{c}}\frac{ z}{2z^{2}+1} dz$ where the contour is the unit circle

Published on 14 May 2016 - 3:03

score 43 · Answer 7 · 2016-05-14 09:23:49

43

Views

complex integrating on half-unit circle

Published on 14 May 2016 - 9:23

score 168 · Answer 8 · 2026-04-01 00:59:13

168

Views

Show that if $ |f( \frac{1}{n}) | \leq \frac{1}{n!}$ then $0$ is an essential singularity

Published on 01 Apr 2026 - 0:59

score 1.4k · Answer 9 · 2016-05-15 12:18:18

1.4k

Views

Prove the integral of $Re(z)$ around a simple closed curve is imaginary

Published on 15 May 2016 - 12:18

score 86 · Answer 10 · 2016-05-15 12:38:29

86

Views

Using residues to compute complex integrals

Published on 15 May 2016 - 12:38

score 22 · Answer 11 · 2016-05-16 08:36:09

22

Views

How to find integrals of the form $\int_{-r}^{+r}\frac{\gamma^{2}-1-y^{2}}{y-z\gamma} dy$

Published on 16 May 2016 - 8:36

score 495 · Answer 12 · 2026-03-25 23:34:55

495

Views

Solution to nonlinear ODE with square root

Published on 25 Mar 2026 - 23:34

score 444 · Answer 13 · 2016-05-16 20:30:13

444

Views

Showing that if $\int_C f(z) \, dz=0$ for every circle $C$ in $\mathbb{C}$, then $f$ is holomorphic.

Published on 16 May 2016 - 20:30

score 796 · Answer 14 · 2016-05-16 22:29:42

796

Views

How do you compute a complex exterior derivative?

Published on 16 May 2016 - 22:29

score 178 · Answer 15 · 2016-05-20 12:43:33

178

Views

Find the complex integral over a path

Published on 20 May 2016 - 12:43

List Question

Why is $\frac{1}{2\pi i}\int_{\gamma}\frac{f'(z)}{f(z)}dz$ an integer?

Suppose that for each $a\in \mathbb{C}$ at least one coefficient of the Taylor's series $f$ about $a$ is zero. Show that $f$ is a polynomial.

Basic contour integral with Cauchy's Residue Theorem

The value of the integral $\int_{C} \dfrac{z^2+1 dz}{(z+1)(z+2)}$ where $C$ is $|z|=\dfrac{3}{2}$

Choice of branch cut

Closed contour integral: $\int_{\mathbb{c}}\frac{ z}{2z^{2}+1} dz$ where the contour is the unit circle

complex integrating on half-unit circle

Show that if $ |f( \frac{1}{n}) | \leq \frac{1}{n!}$ then $0$ is an essential singularity

Prove the integral of $Re(z)$ around a simple closed curve is imaginary

Using residues to compute complex integrals

How to find integrals of the form $\int_{-r}^{+r}\frac{\gamma^{2}-1-y^{2}}{y-z\gamma} dy$

Solution to nonlinear ODE with square root

Showing that if $\int_C f(z) \, dz=0$ for every circle $C$ in $\mathbb{C}$, then $f$ is holomorphic.

How do you compute a complex exterior derivative?

Find the complex integral over a path

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