List questions from laurent-series

Published on 17 Mar 2026 - 16:42

355

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How do I show with Laurent Series Expansion that $1/z$ has a simple pole for $z=z_0=0$?

Published on 17 Mar 2026 - 13:52

2.5k

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Order of Poles of $1/\cos(1/z)$

Published on 23 Mar 2026 - 6:03

2k

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Classification of singularities of $\sin\left( \frac{1}{\sin(\frac{1}{z})}\right)$

Published on 24 Mar 2026 - 15:36

172

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Laurent expansion and singularities of $\frac{1-\cos(z)}{e^{2iz}-1}$

Published on 23 Mar 2026 - 22:28

529

Views

Laurent Series problems

Published on 25 Mar 2026 - 13:05

1.2k

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Laurent series VS Fourier series.

Published on 25 Mar 2026 - 3:44

473

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Laurent series and radius of convergence of $f(z)=\frac{1}{(1-\cosh z)^2}$

Published on 25 Mar 2026 - 18:29

729

Views

Show that a localization a power series ring $R[[x]]$ by $S$ can be written a certain way.

Published on 17 Mar 2026 - 5:49

274

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Laurent series of complex function

Published on 21 Mar 2026 - 22:31

73

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Calculate $\int_{\gamma} \frac{z^2}{\sin(z^3)} dz $ where $\gamma=\{z \in \mathbb{C} : |z|=\frac{3}{2}\}$

Published on 20 Mar 2026 - 8:28

65

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Recurrence relation to extract coefficients $\frac{1}{z^3+z+2}=\sum_{n=-\infty}^\infty (z+1)^n c_n$

Published on 25 Mar 2026 - 17:21

190

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Finding the residue of essential singularities

Published on 24 Mar 2026 - 20:41

1.6k

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Laurent series expansion about z=0

Published on 25 Mar 2026 - 17:26

246

Views

Laurent series region of convergence

Published on 25 Mar 2026 - 17:22

List Question

Find Laurent series of rational function $f(z)={1 \over (z+1)^2(z+2)}$

How do I show with Laurent Series Expansion that $1/z$ has a simple pole for $z=z_0=0$?

Order of Poles of $1/\cos(1/z)$

Classification of singularities of $\sin\left( \frac{1}{\sin(\frac{1}{z})}\right)$

Laurent expansion and singularities of $\frac{1-\cos(z)}{e^{2iz}-1}$

Laurent Series problems

Laurent series VS Fourier series.

Laurent series and radius of convergence of $f(z)=\frac{1}{(1-\cosh z)^2}$

Show that a localization a power series ring $R[[x]]$ by $S$ can be written a certain way.

Laurent series of complex function

Calculate $\int_{\gamma} \frac{z^2}{\sin(z^3)} dz $ where $\gamma=\{z \in \mathbb{C} : |z|=\frac{3}{2}\}$

Recurrence relation to extract coefficients $\frac{1}{z^3+z+2}=\sum_{n=-\infty}^\infty (z+1)^n c_n$

Finding the residue of essential singularities

Laurent series expansion about z=0

Laurent series region of convergence

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