Question

Showing holomorphicity of $f(z)=\sum_{n\ge 1} \frac{(z-n)^{-n}}{n!}$ on $\mathbb{C}\setminus \mathbb{N}$

score 40 · Answer 1 · 2023-06-21 22:40:56

40

Views

Showing holomorphicity of $f(z)=\sum_{n\ge 1} \frac{(z-n)^{-n}}{n!}$ on $\mathbb{C}\setminus \mathbb{N}$

Published on 21 Jun 2023 - 22:40

score 311 · Answer 2 · 2023-06-25 09:31:31

311

Views

Integral using Bessel functions $\int_0^{\pi}\cos⁡(z\sin x)e^{\cos (x)}\ dx$

Published on 25 Jun 2023 - 9:31

score 69 · Answer 3 · 2023-07-02 02:50:12

69

Views

Clarification on Laurent series expansion exercise

Published on 02 Jul 2023 - 2:50

score 81 · Answer 4 · 2026-03-27 22:03:07

81

Views

How can $1/f(z)$ have a zero?

Published on 27 Mar 2026 - 22:03

score 31 · Answer 5 · 2026-03-27 13:47:33

31

Views

What prerequisites do I need to understand the insertion of a lag-operator for a complex dummy z

Published on 27 Mar 2026 - 13:47

score 36 · Answer 6 · 2023-07-06 14:25:07

36

Views

Laurent series of real part of holomorphic function

Published on 06 Jul 2023 - 14:25

score 58 · Answer 7 · 2026-03-26 12:50:36

58

Views

Decomposition of the field of Laurent formal power series in a polynomial ring and a formal power series ring

Published on 26 Mar 2026 - 12:50

score 39 · Answer 8 · 2026-03-29 06:55:22

39

Views

Ring of formal multivariate Laurent series as a consecutive localisation

Published on 29 Mar 2026 - 6:55

score 29 · Answer 9 · 2023-07-17 09:18:22

29

Views

Find coefficients of Laurentseries

Published on 17 Jul 2023 - 9:18

score 129 · Answer 10 · 2026-03-27 20:21:10

129

Views

Poles and the Laurent series for $\frac{1}{z^4-1}$

Published on 27 Mar 2026 - 20:21

score 156 · Answer 11 · 2023-07-25 01:32:16

156

Views

Contour Integral around the unit circle $C$: $\oint_C \frac{e^z-1}{\sin^3(z)}dz$

Published on 25 Jul 2023 - 1:32

score 40 · Answer 12 · 2026-03-27 20:12:16

40

Views

Laurent Expansion at specific singularity

Published on 27 Mar 2026 - 20:12

score 66 · Answer 13 · 2023-08-07 15:56:01

66

Views

Find the laurent series of the function $f(z) = \frac{1}{(z+i)(z-5i)}$ which is valid in the annulus where $1 < |z| < 5$

Published on 07 Aug 2023 - 15:56

score 61 · Answer 14 · 2023-08-08 04:15:18

61

Views

Laurent series of the function $f(z)=\frac{1}{z^2(e^{z}-e^{-z})}$

Published on 08 Aug 2023 - 4:15

score 42 · Answer 15 · 2026-03-27 04:17:02

42

Views

Expansion of Beta function near negative integers

Published on 27 Mar 2026 - 4:17

List Question

Showing holomorphicity of $f(z)=\sum_{n\ge 1} \frac{(z-n)^{-n}}{n!}$ on $\mathbb{C}\setminus \mathbb{N}$

Integral using Bessel functions $\int_0^{\pi}\cos⁡(z\sin x)e^{\cos (x)}\ dx$

Clarification on Laurent series expansion exercise

How can $1/f(z)$ have a zero?

What prerequisites do I need to understand the insertion of a lag-operator for a complex dummy z

Laurent series of real part of holomorphic function

Decomposition of the field of Laurent formal power series in a polynomial ring and a formal power series ring

Ring of formal multivariate Laurent series as a consecutive localisation

Find coefficients of Laurentseries

Poles and the Laurent series for $\frac{1}{z^4-1}$

Contour Integral around the unit circle $C$: $\oint_C \frac{e^z-1}{\sin^3(z)}dz$

Laurent Expansion at specific singularity

Find the laurent series of the function $f(z) = \frac{1}{(z+i)(z-5i)}$ which is valid in the annulus where $1 < |z| < 5$

Laurent series of the function $f(z)=\frac{1}{z^2(e^{z}-e^{-z})}$

Expansion of Beta function near negative integers

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