Question

Kind of singularity with Laurent series of $f(z)=\frac{1}{1+2z}$

score 59 · Answer 1 · 2026-03-30 14:22:20

59

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Kind of singularity with Laurent series of $f(z)=\frac{1}{1+2z}$

Published on 30 Mar 2026 - 14:22

score 25 · Answer 2 · 2026-03-28 08:50:09

25

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Field of formal Laurent series as a colimit of fractions

Published on 28 Mar 2026 - 8:50

score 62 · Answer 3 · 2022-08-08 16:00:34

62

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find the Laurent series expansion of $f(z) = \frac{1}{(z + 1)(z +3)}$ for the region $0 \lt |{z + 1}| \lt 2$

Published on 08 Aug 2022 - 16:00

score 46 · Answer 4 · 2022-08-09 22:17:43

46

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Define the term $a_n$ in Laurent's series expansion $\sum_{n=-\infty}^{\infty} a_n(z-a)^n$ of $f$ centered on $z=a.$...

Published on 09 Aug 2022 - 22:17

score 214 · Answer 5 · 2026-03-30 06:49:23

214

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Given a laurent series, how do we show it doesnt have a pole?

Published on 30 Mar 2026 - 6:49

score 44 · Answer 6 · 2022-08-10 21:01:26

44

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Radius of convergence for this series

Published on 10 Aug 2022 - 21:01

score 75 · Answer 7 · 2026-03-28 06:59:50

75

Views

Relating the coefficients of Laurent series to that of power series.

Published on 28 Mar 2026 - 6:59

score 72 · Answer 8 · 2022-08-22 22:36:32

72

Views

When do log-series go laurent and why?

Published on 22 Aug 2022 - 22:36

score 464 · Answer 9 · 2022-08-23 16:46:24

464

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Why does the Laurent series require negative powers in order to represent complex functions?

Published on 23 Aug 2022 - 16:46

score 52 · Answer 10 · 2026-04-01 07:15:45

52

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Clarification on proof of Laurent development (Conway)

Published on 01 Apr 2026 - 7:15

score 110 · Answer 11 · 2022-08-27 04:15:45

110

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$\pi^2 \frac{\cos(\pi z)}{\sin^{2}(\pi z)} = \sum_{n \in \mathbb{Z}} \frac{(-1)^n}{(z-n)^2}$

Published on 27 Aug 2022 - 4:15

score 53 · Answer 12 · 2026-03-25 13:55:19

53

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Formal completion of a scalar extension

Published on 25 Mar 2026 - 13:55

score 207 · Answer 13 · 2022-09-04 08:31:56

207

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Extensions of the field $k((x))$ of Laurent series

Published on 04 Sep 2022 - 8:31

score 49 · Answer 14 · 2022-09-04 19:12:03

49

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What is the difference between these two Laurent series expansions

Published on 04 Sep 2022 - 19:12

score 75 · Answer 15 · 2026-02-23 12:54:41

75

Views

Rearrange terms in products of power series

Published on 23 Feb 2026 - 12:54

List Question

Kind of singularity with Laurent series of $f(z)=\frac{1}{1+2z}$

Field of formal Laurent series as a colimit of fractions

find the Laurent series expansion of $f(z) = \frac{1}{(z + 1)(z +3)}$ for the region $0 \lt |{z + 1}| \lt 2$

Define the term $a_n$ in Laurent's series expansion $\sum_{n=-\infty}^{\infty} a_n(z-a)^n$ of $f$ centered on $z=a.$...

Given a laurent series, how do we show it doesnt have a pole?

Radius of convergence for this series

Relating the coefficients of Laurent series to that of power series.

When do log-series go laurent and why?

Why does the Laurent series require negative powers in order to represent complex functions?

Clarification on proof of Laurent development (Conway)

$\pi^2 \frac{\cos(\pi z)}{\sin^{2}(\pi z)} = \sum_{n \in \mathbb{Z}} \frac{(-1)^n}{(z-n)^2}$

Formal completion of a scalar extension

Extensions of the field $k((x))$ of Laurent series

What is the difference between these two Laurent series expansions

Rearrange terms in products of power series

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