Question

Find residues of a function $f(z) = z^{10}e^{\frac{1}{2z}} + \frac{z+4\pi}{z-4\pi}\cot{\frac{z}{2}}$

score 107 · Answer 1 · 2019-06-13 18:52:03

107

Views

Find residues of a function $f(z) = z^{10}e^{\frac{1}{2z}} + \frac{z+4\pi}{z-4\pi}\cot{\frac{z}{2}}$

Published on 13 Jun 2019 - 18:52

score 697 · Answer 2 · 2026-03-25 05:02:13

697

Views

Prove that a function that is analytic everywhere except a finite number of poles is rational

Published on 25 Mar 2026 - 5:02

score 26 · Answer 3 · 2019-06-18 08:52:54

26

Views

$f(z)=\frac{\sin^{2014}(z) e^{\frac{1}{(z-10)^2}}}{(z-2i)^8(z-2014\pi)^2}$ Find the type of singularity $z=2014\pi$

Published on 18 Jun 2019 - 8:52

score 73 · Answer 4 · 2019-06-18 14:58:09

73

Views

Calculate and decide the type of the singularities of the function $\frac{z^2}{1-e^{z^3}}$

Published on 18 Jun 2019 - 14:58

score 298 · Answer 5 · 2019-06-19 09:44:41

298

Views

Finding the singularities of a function with a square root

Published on 19 Jun 2019 - 9:44

score 807 · Answer 6 · 2019-06-19 12:00:44

807

Views

Classify the isolated singularities of $ \frac{z^5}{z^3 + z} $ and $ \frac{\cos z}{z^2 -1} $

Published on 19 Jun 2019 - 12:00

score 165 · Answer 7 · 2019-06-20 03:23:01

165

Views

Prove that the limit of zeroes of a non zero complex valued function is an essential singularity of the function

Published on 20 Jun 2019 - 3:23

score 103 · Answer 8 · 2026-03-25 01:31:59

103

Views

Series representation and isolated singularity

Published on 25 Mar 2026 - 1:31

score 129 · Answer 9 · 2026-03-22 16:43:44

129

Views

Using implicit function theorem to solve singularity on a curve in $\mathbb{R}^2$

Published on 22 Mar 2026 - 16:43

score 382 · Answer 10 · 2019-06-30 07:07:23

382

Views

Singularity/residue of $\frac{z}{\sin(z)}$

Published on 30 Jun 2019 - 7:07

score 1.8k · Answer 11 · 2019-07-01 08:54:47

1.8k

Views

If $f$ and $g$ have poles of order $m,n$ respectively, what is the pole order of $f/g$?

Published on 01 Jul 2019 - 8:54

score 3.3k · Answer 12 · 2019-07-01 12:51:15

3.3k

Views

Residue of $\sin (1/z)$ in $z=0$

Published on 01 Jul 2019 - 12:51

score 54 · Answer 13 · 2019-07-01 17:11:31

54

Views

Determine the character of all singularities of function: $g(z)= \frac{1}{e^{z^{2}} -1}.$

Published on 01 Jul 2019 - 17:11

score 401 · Answer 14 · 2019-07-01 20:28:12

401

Views

Infinitely many singularities inside the contour with residue theorem

Published on 01 Jul 2019 - 20:28

score 492 · Answer 15 · 2019-07-02 15:36:51

492

Views

$f$ is holomorphic in $B(z_0,r)\setminus\{z_0\}$ and does not except real values. Then $z_0$ is a removable singularity

Published on 02 Jul 2019 - 15:36

List Question

Find residues of a function $f(z) = z^{10}e^{\frac{1}{2z}} + \frac{z+4\pi}{z-4\pi}\cot{\frac{z}{2}}$

Prove that a function that is analytic everywhere except a finite number of poles is rational

$f(z)=\frac{\sin^{2014}(z) e^{\frac{1}{(z-10)^2}}}{(z-2i)^8(z-2014\pi)^2}$ Find the type of singularity $z=2014\pi$

Calculate and decide the type of the singularities of the function $\frac{z^2}{1-e^{z^3}}$

Finding the singularities of a function with a square root

Classify the isolated singularities of $ \frac{z^5}{z^3 + z} $ and $ \frac{\cos z}{z^2 -1} $

Prove that the limit of zeroes of a non zero complex valued function is an essential singularity of the function

Series representation and isolated singularity

Using implicit function theorem to solve singularity on a curve in $\mathbb{R}^2$

Singularity/residue of $\frac{z}{\sin(z)}$

If $f$ and $g$ have poles of order $m,n$ respectively, what is the pole order of $f/g$?

Residue of $\sin (1/z)$ in $z=0$

Determine the character of all singularities of function: $g(z)= \frac{1}{e^{z^{2}} -1}.$

Infinitely many singularities inside the contour with residue theorem

$f$ is holomorphic in $B(z_0,r)\setminus\{z_0\}$ and does not except real values. Then $z_0$ is a removable singularity

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