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Laurent series Approximation in Algebraic Curves

score 129 · Answer 1 · 2026-03-28 00:54:18

129

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Laurent series Approximation in Algebraic Curves

Published on 28 Mar 2026 - 0:54

score 97 · Answer 2 · 2020-05-13 06:17:16

97

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Find the Laurent series at z=0

Published on 13 May 2020 - 6:17

score 26 · Answer 3 · 2020-05-13 17:03:17

26

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$a_{−3}$ in the Laurent expansion of $f(z)$ in the region $0 < |z| < 1$. $f(z)=\frac{1}{2z^3}-\frac{1}{z^3+i}$

Published on 13 May 2020 - 17:03

score 77 · Answer 4 · 2020-05-14 18:23:46

77

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Can you find a residue by using Taylor's formula for a single coefficient instead of expanding into a Laurent series?

Published on 14 May 2020 - 18:23

score 1.3k · Answer 5 · 2020-05-17 16:55:59

1.3k

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Laurent series of $f(z)=\frac{1}{z^{2}\sinh(z)}$

Published on 17 May 2020 - 16:55

score 38 · Answer 6 · 2020-05-18 14:55:56

38

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Finding Laurent series of $f(z) = \frac{1}{z^{2}+4}$ on two different domains.

Published on 18 May 2020 - 14:55

score 43 · Answer 7 · 2020-05-18 21:59:12

43

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Laurent series for $ f(z) = \frac{1} {z} + \frac{1} {(1-z)} + \frac{1} {(2-z)} $ around arround $0< |z|<1, 0< |z-1|<1$ and $0< |z|<2$?

Published on 18 May 2020 - 21:59

score 24 · Answer 8 · 2020-05-19 13:42:49

24

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Use Laurent Series to Determine Bi-Analytic Function

Published on 19 May 2020 - 13:42

score 27 · Answer 9 · 2026-03-28 00:56:21

27

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Showing by Hand that $H^1(0)=0 , H^1(-p)=0$ in $\mathbb{C}$ , Mittag-Leffer Problems in $\mathbb{C}$ and $\mathbb{C}/L$

Published on 28 Mar 2026 - 0:56

score 31 · Answer 10 · 2020-05-22 04:55:14

31

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Alternative Laurent expansion of $1-e^{-x}$

Published on 22 May 2020 - 4:55

score 91 · Answer 11 · 2020-05-23 06:08:15

91

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Finding the Laurent expansion

Published on 23 May 2020 - 6:08

score 119 · Answer 12 · 2026-03-25 06:02:00

119

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Does this strategy of characterizing poles always work?

Published on 25 Mar 2026 - 6:02

score 181 · Answer 13 · 2020-05-24 09:48:32

181

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Determine convergence annulus of Laurent series without computing the Laurent series

Published on 24 May 2020 - 9:48

score 252 · Answer 14 · 2020-05-24 22:10:11

252

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What is the residue of $f(z) = z\sin(z + {1 \over z})$ at $z_0 = 0$?

Published on 24 May 2020 - 22:10

score 163 · Answer 15 · 2020-05-28 18:45:59

163

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Use the Laurent series to prove that $\int_{0}^{2 \pi} e^{\cos(t)} \cos(nt-\sin t)\,dt=\frac{2 \pi}{n!}$

Published on 28 May 2020 - 18:45

List Question

Laurent series Approximation in Algebraic Curves

Find the Laurent series at z=0

$a_{−3}$ in the Laurent expansion of $f(z)$ in the region $0 < |z| < 1$. $f(z)=\frac{1}{2z^3}-\frac{1}{z^3+i}$

Can you find a residue by using Taylor's formula for a single coefficient instead of expanding into a Laurent series?

Laurent series of $f(z)=\frac{1}{z^{2}\sinh(z)}$

Finding Laurent series of $f(z) = \frac{1}{z^{2}+4}$ on two different domains.

Laurent series for $ f(z) = \frac{1} {z} + \frac{1} {(1-z)} + \frac{1} {(2-z)} $ around arround $0< |z|<1, 0< |z-1|<1$ and $0< |z|<2$?

Use Laurent Series to Determine Bi-Analytic Function

Showing by Hand that $H^1(0)=0 , H^1(-p)=0$ in $\mathbb{C}$ , Mittag-Leffer Problems in $\mathbb{C}$ and $\mathbb{C}/L$

Alternative Laurent expansion of $1-e^{-x}$

Finding the Laurent expansion

Does this strategy of characterizing poles always work?

Determine convergence annulus of Laurent series without computing the Laurent series

What is the residue of $f(z) = z\sin(z + {1 \over z})$ at $z_0 = 0$?

Use the Laurent series to prove that $\int_{0}^{2 \pi} e^{\cos(t)} \cos(nt-\sin t)\,dt=\frac{2 \pi}{n!}$

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