Question

Evaluate $\int_{|z|=1}\frac{|dz|}{|z-a|^2}$ using Cauchy's Theorem.

score 111 · Answer 1 · 2016-03-30 20:29:16

111

Views

Evaluate $\int_{|z|=1}\frac{|dz|}{|z-a|^2}$ using Cauchy's Theorem.

Published on 30 Mar 2016 - 20:29

score 1.2k · Answer 2 · 2016-03-30 21:30:35

1.2k

Views

Use result that composition of analytic functions is harmonic to find harmonic conjugate of $e^{-2xy}\sin (x^{2}-y^{2})$

Published on 30 Mar 2016 - 21:30

score 344 · Answer 3 · 2016-04-03 21:22:34

344

Views

The existence of the roots of an holomorphic function on an open connected domain

Published on 03 Apr 2016 - 21:22

score 586 · Answer 4 · 2016-04-09 08:54:03

586

Views

Power of a function is analytic

Published on 09 Apr 2016 - 8:54

score 120 · Answer 5 · 2016-04-10 19:02:58

120

Views

Laurent expansion

Published on 10 Apr 2016 - 19:02

score 85 · Answer 6 · 2026-03-11 11:23:37

85

Views

How to prove this function $f(x):= \sum_{k=1}^\infty \frac{1}{k^k} \exp(2\pi \, i\,k\,x)$ is entire?

Published on 11 Mar 2026 - 11:23

score 104 · Answer 7 · 2016-04-11 13:58:40

104

Views

Why is this point analytic?

Published on 11 Apr 2016 - 13:58

score 1.4k · Answer 8 · 2016-04-11 17:27:32

1.4k

Views

Laurent expansion of $\frac{1}{\sin z}$

Published on 11 Apr 2016 - 17:27

score 157 · Answer 9 · 2016-04-12 22:58:04

157

Views

Local Uniform Convergence and Composition

Published on 12 Apr 2016 - 22:58

score 405 · Answer 10 · 2016-04-15 10:02:42

405

Views

Interior Uniqueness: Does there exist an analytic function on a neighborhood of $z=0$ that satisfies the following?

Published on 15 Apr 2016 - 10:02

score 160 · Answer 11 · 2016-04-15 16:18:35

160

Views

Application of Schawarz lemma??

Published on 15 Apr 2016 - 16:18

score 408 · Answer 12 · 2016-04-15 20:25:06

408

Views

Analytic, non- constant complex function has finitely many zeros inside the disk $D(0, R)$ for all $R > 0$

Published on 15 Apr 2016 - 20:25

score 1.7k · Answer 13 · 2016-04-17 14:29:03

1.7k

Views

Let $f$ be analytic on the unit disk $D = \{z : |z| ≤ 1\}$ and suppose $Im(f(z)) > 0$ for $z ∈ D$ and $f(0) = i$. Prove that $|f ' (0)| ≤ 1$.

Published on 17 Apr 2016 - 14:29

score 43 · Answer 14 · 2016-04-18 15:34:52

43

Views

Is this function analytic: $F(x+iy)=\frac1{\pi}\int_{\mathbb R}\frac y{(x-t)^2+y^2}\,f(t)\,dt$.?

Published on 18 Apr 2016 - 15:34

score 469 · Answer 15 · 2016-04-18 17:16:48

469

Views

Function analytic in each variable does not imply jointly analytic

Published on 18 Apr 2016 - 17:16

List Question

Evaluate $\int_{|z|=1}\frac{|dz|}{|z-a|^2}$ using Cauchy's Theorem.

Use result that composition of analytic functions is harmonic to find harmonic conjugate of $e^{-2xy}\sin (x^{2}-y^{2})$

The existence of the roots of an holomorphic function on an open connected domain

Power of a function is analytic

Laurent expansion

How to prove this function $f(x):= \sum_{k=1}^\infty \frac{1}{k^k} \exp(2\pi \, i\,k\,x)$ is entire?

Why is this point analytic?

Laurent expansion of $\frac{1}{\sin z}$

Local Uniform Convergence and Composition

Interior Uniqueness: Does there exist an analytic function on a neighborhood of $z=0$ that satisfies the following?

Application of Schawarz lemma??

Analytic, non- constant complex function has finitely many zeros inside the disk $D(0, R)$ for all $R > 0$

Let $f$ be analytic on the unit disk $D = \{z : |z| ≤ 1\}$ and suppose $Im(f(z)) > 0$ for $z ∈ D$ and $f(0) = i$. Prove that $|f ' (0)| ≤ 1$.

Is this function analytic: $F(x+iy)=\frac1{\pi}\int_{\mathbb R}\frac y{(x-t)^2+y^2}\,f(t)\,dt$.?

Function analytic in each variable does not imply jointly analytic

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