Question

Why does using the Laurent series for $\frac{\cos 2z}{z^2}$ give a different residue than taking the real part of $e^{i2z}/{z^2}?$

score 134 · Answer 1 · 2022-09-23 05:03:57

134

Views

Why does using the Laurent series for $\frac{\cos 2z}{z^2}$ give a different residue than taking the real part of $e^{i2z}/{z^2}?$

Published on 23 Sep 2022 - 5:03

score 31 · Answer 2 · 2022-09-26 15:09:48

31

Views

Trouble with determining the Laurent series for $f(z)=z^{-1}+(z+1)^{-1}+(z+2)^{-1}$ on the annulus $\{z\mid 0<|z|<1\}$ with the by the book method

Published on 26 Sep 2022 - 15:09

score 111 · Answer 3 · 2022-09-29 08:51:43

111

Views

Why do we choose $\frac{1}{1-z} = 1 + z + z^2 + \cdots$ instead of $\frac{1}{1-z} = z + z^2 +\cdots$?

Published on 29 Sep 2022 - 8:51

score 31 · Answer 4 · 2022-09-29 15:33:20

31

Views

Finding the Laurent series of the function $f(z) = \frac{1 - 2z}{(z^2 - z)^2}$ on the annulus $\Delta^*(0,1)$ (i.e. $0 < |z| < 1$)

Published on 29 Sep 2022 - 15:33

score 198 · Answer 5 · 2022-09-29 16:02:32

198

Views

Intuition behind Laurent series expansion

Published on 29 Sep 2022 - 16:02

score 123 · Answer 6 · 2022-10-11 19:00:27

123

Views

Laurent series expansion of $\frac{1}{z(z-2)^2}$ at $z=2$

Published on 11 Oct 2022 - 19:00

score 17 · Answer 7 · 2022-10-12 10:45:24

17

Views

How to get the weak (p,q) condition of the complex ordinary differential equation?

Published on 12 Oct 2022 - 10:45

score 54 · Answer 8 · 2022-10-14 01:09:56

54

Views

Laurent series expansion $\exp({\frac{1}{z^4}})$

Published on 14 Oct 2022 - 1:09

score 109 · Answer 9 · 2022-10-14 20:40:07

109

Views

Closed form for $\sum_{n=1}^\infty \frac{x^2}{\sinh^2(xn)}$

Published on 14 Oct 2022 - 20:40

score 46 · Answer 10 · 2022-10-20 16:52:06

46

Views

routin answer for $\sum_{i=1}^{n} \frac{1}{i^{2}}$

Published on 20 Oct 2022 - 16:52

score 70 · Answer 11 · 2022-10-21 23:18:07

70

Views

find the Laurent series of $\frac{3}{2+z-z^2}$ about the following domains

Published on 21 Oct 2022 - 23:18

score 141 · Answer 12 · 2026-03-28 10:27:18

141

Views

The field of formal laurent series viewed as a polynomial ring

Published on 28 Mar 2026 - 10:27

score 80 · Answer 13 · 2022-11-01 00:30:13

80

Views

Find the Laurent series expansion of $\frac{1}{z(e^z-1)}$ and show that it has a pole of second order at $z = 0$.

Published on 01 Nov 2022 - 0:30

score 49 · Answer 14 · 2026-03-30 16:04:37

49

Views

Residue of essential singularity with exp

Published on 30 Mar 2026 - 16:04

score 64 · Answer 15 · 2026-04-01 10:28:01

64

Views

Find all analytic functions $f: \mathbb{C} \backslash\{3\} \rightarrow \mathbb{C}$ such that $|f(z)| \leq \frac{\left|(z-2)^{2}\right|}{|z-3|}$

Published on 01 Apr 2026 - 10:28

List Question

Why does using the Laurent series for $\frac{\cos 2z}{z^2}$ give a different residue than taking the real part of $e^{i2z}/{z^2}?$

Trouble with determining the Laurent series for $f(z)=z^{-1}+(z+1)^{-1}+(z+2)^{-1}$ on the annulus $\{z\mid 0<|z|<1\}$ with the by the book method

Why do we choose $\frac{1}{1-z} = 1 + z + z^2 + \cdots$ instead of $\frac{1}{1-z} = z + z^2 +\cdots$?

Finding the Laurent series of the function $f(z) = \frac{1 - 2z}{(z^2 - z)^2}$ on the annulus $\Delta^*(0,1)$ (i.e. $0 < |z| < 1$)

Intuition behind Laurent series expansion

Laurent series expansion of $\frac{1}{z(z-2)^2}$ at $z=2$

How to get the weak (p,q) condition of the complex ordinary differential equation?

Laurent series expansion $\exp({\frac{1}{z^4}})$

Closed form for $\sum_{n=1}^\infty \frac{x^2}{\sinh^2(xn)}$

routin answer for $\sum_{i=1}^{n} \frac{1}{i^{2}}$

find the Laurent series of $\frac{3}{2+z-z^2}$ about the following domains

The field of formal laurent series viewed as a polynomial ring

Find the Laurent series expansion of $\frac{1}{z(e^z-1)}$ and show that it has a pole of second order at $z = 0$.

Residue of essential singularity with exp

Find all analytic functions $f: \mathbb{C} \backslash\{3\} \rightarrow \mathbb{C}$ such that $|f(z)| \leq \frac{\left|(z-2)^{2}\right|}{|z-3|}$

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