Question

How to find the largest $R$ such that the Laurent series of $f(z)=\frac{2}{(z^-1)}+\frac{3}{2z-i}$ about $z=1$ converges for $0<|z-1|<R$?

score 1k · Answer 1 · 2016-04-22 21:12:09

How to find the largest $R$ such that the Laurent series of $f(z)=\frac{2}{(z^-1)}+\frac{3}{2z-i}$ about $z=1$ converges for $0<|z-1|<R$?

score 693 · Answer 2 · 2016-04-24 18:22:23

693

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Determine the singular part of $f$ at these poles.

Published on 24 Apr 2016 - 18:22

score 858 · Answer 3 · 2026-03-27 16:22:51

858

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$f$ has pole of order $m$ and $g$ has a pole of order $n$ at $z_{0}$, show $f+g$ has isolated singular point there

Published on 27 Mar 2026 - 16:22

score 833 · Answer 4 · 2026-03-28 06:09:44

833

Views

Find and classify singular points of $\cot\left(\frac{1}{z}\right)$

Published on 28 Mar 2026 - 6:09

score 37 · Answer 5 · 2016-04-26 22:49:54

37

Views

$g(z)=\frac{1}{3-z}$ - Laurent series for two differents annulus

Published on 26 Apr 2016 - 22:49

score 191 · Answer 6 · 2016-04-27 06:48:56

191

Views

Finding Laurent series

Published on 27 Apr 2016 - 6:48

score 64 · Answer 7 · 2016-04-27 13:43:45

64

Views

principle laurent series of $f(z)=\frac{(e^z-1)(1-\cos(2z))}{z^4\sin(z)}$ at $z=0$ and determine $\oint_{|z|=1} f(z)dz$.

Published on 27 Apr 2016 - 13:43

score 66 · Answer 8 · 2016-04-27 19:00:21

66

Views

Determine the Laurent expansion of $f(z)=\frac{z}{(z-1)(2-z)}$ for different regions in the complex plane.

Published on 27 Apr 2016 - 19:00

score 68 · Answer 9 · 2016-04-27 21:05:39

68

Views

Using the $\cot (\pi z)$ to find $\sum \frac{1}{n^2}$

Published on 27 Apr 2016 - 21:05

score 341 · Answer 10 · 2016-04-28 00:19:57

341

Views

Expand the Laurent series

Published on 28 Apr 2016 - 0:19

score 98 · Answer 11 · 2016-04-28 02:19:28

98

Views

What is the Laurent expansion of $f(z)=\frac1{z-3}$?

Published on 28 Apr 2016 - 2:19

score 95 · Answer 12 · 2016-04-28 10:29:05

95

Views

Find the first terms of the Laurent series for: $\frac{e^{\frac{1}{z}}}{z^2-1}$

Published on 28 Apr 2016 - 10:29

score 578 · Answer 13 · 2016-04-28 11:02:01

578

Views

Finding the Laurent Series for $\frac{1}{e^z-1}$ for $0<|z|<2\pi$

Published on 28 Apr 2016 - 11:02

score 75 · Answer 14 · 2016-04-28 15:28:58

75

Views

Finding Possible Meromorphic functions on $\mathbb{C}$

Published on 28 Apr 2016 - 15:28

score 1.5k · Answer 15 · 2026-02-23 09:33:46

1.5k

Views

Laurent series for $f(z) = \exp(z+\frac{1}{z})$ around $0$

Published on 23 Feb 2026 - 9:33

List Question

How to find the largest $R$ such that the Laurent series of $f(z)=\frac{2}{(z^-1)}+\frac{3}{2z-i}$ about $z=1$ converges for $0<|z-1|<R$?

Determine the singular part of $f$ at these poles.

$f$ has pole of order $m$ and $g$ has a pole of order $n$ at $z_{0}$, show $f+g$ has isolated singular point there

Find and classify singular points of $\cot\left(\frac{1}{z}\right)$

$g(z)=\frac{1}{3-z}$ - Laurent series for two differents annulus

Finding Laurent series

principle laurent series of $f(z)=\frac{(e^z-1)(1-\cos(2z))}{z^4\sin(z)}$ at $z=0$ and determine $\oint_{|z|=1} f(z)dz$.

Determine the Laurent expansion of $f(z)=\frac{z}{(z-1)(2-z)}$ for different regions in the complex plane.

Using the $\cot (\pi z)$ to find $\sum \frac{1}{n^2}$

Expand the Laurent series

What is the Laurent expansion of $f(z)=\frac1{z-3}$?

Find the first terms of the Laurent series for: $\frac{e^{\frac{1}{z}}}{z^2-1}$

Finding the Laurent Series for $\frac{1}{e^z-1}$ for $0<|z|<2\pi$

Finding Possible Meromorphic functions on $\mathbb{C}$

Laurent series for $f(z) = \exp(z+\frac{1}{z})$ around $0$

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