Question

How can I show that this meromorphic function is a rational function of two polynomials?

score 858 · Answer 1 · 2026-03-09 20:29:09

858

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How can I show that this meromorphic function is a rational function of two polynomials?

Published on 09 Mar 2026 - 20:29

score 75 · Answer 2 · 2015-12-01 07:35:49

75

Views

If $f$ is analytic and $f(0)=a_0$ then prove that $|\lambda| \ge \frac{|a_0|}{M}$.

Published on 01 Dec 2015 - 7:35

score 982 · Answer 3 · 2015-12-02 03:13:29

982

Views

Is my idea of decomposing a meromorphic function into a sum of Laurent series correct?

Published on 02 Dec 2015 - 3:13

score 120 · Answer 4 · 2026-02-23 12:31:56

120

Views

Cesaro limit of analytic functions

Published on 23 Feb 2026 - 12:31

score 258 · Answer 5 · 2015-12-05 18:01:51

258

Views

Prove a function to be analytic by dominated convergence theorem

Published on 05 Dec 2015 - 18:01

score 888 · Answer 6 · 2015-12-05 19:27:17

Show that there exists $g: \mathbb{\Omega} \rightarrow \mathbb{C}$ analytic such that $g(z)^n = f(z)$ for all $z \in \mathbb{\Omega}$

score 169 · Answer 7 · 2015-12-06 03:37:33

169

Views

Multisection of a Power Series Proof

Published on 06 Dec 2015 - 3:37

score 271 · Answer 8 · 2015-12-06 16:47:16

271

Views

If $F$ is analytic and injective on the unit disc and $B(F(0), |F'(0)|)\subseteq F(B(0,1))$, then $F(z)= F(0) + F'(0)z$.

Published on 06 Dec 2015 - 16:47

score 69 · Answer 9 · 2015-12-07 02:00:09

69

Views

Finding analyticity

Published on 07 Dec 2015 - 2:00

score 39 · Answer 10 · 2015-12-11 16:58:01

39

Views

Complex inequalities and constants

Published on 11 Dec 2015 - 16:58

score 108 · Answer 11 · 2015-12-12 10:11:49

108

Views

Mapping the region $\Gamma_{z}$ using the conformal map $ \omega=\frac{-2z}{z^{2}+1}$

Published on 12 Dec 2015 - 10:11

score 73 · Answer 12 · 2015-12-12 13:51:02

73

Views

Analytic functions and constants: Proving $f(z)-g(z)$ is constant

Published on 12 Dec 2015 - 13:51

score 713 · Answer 13 · 2015-12-12 20:13:30

713

Views

An entire function bounded outside a strip which contains the reals is constant

Published on 12 Dec 2015 - 20:13

score 34 · Answer 14 · 2015-12-13 20:54:24

34

Views

Singularities of difference of two functions

Published on 13 Dec 2015 - 20:54

score 115 · Answer 15 · 2015-12-16 18:58:22

115

Views

Convergence and analyticity of functions

Published on 16 Dec 2015 - 18:58

List Question

How can I show that this meromorphic function is a rational function of two polynomials?

If $f$ is analytic and $f(0)=a_0$ then prove that $|\lambda| \ge \frac{|a_0|}{M}$.

Is my idea of decomposing a meromorphic function into a sum of Laurent series correct?

Cesaro limit of analytic functions

Prove a function to be analytic by dominated convergence theorem

Show that there exists $g: \mathbb{\Omega} \rightarrow \mathbb{C}$ analytic such that $g(z)^n = f(z)$ for all $z \in \mathbb{\Omega}$

Multisection of a Power Series Proof

If $F$ is analytic and injective on the unit disc and $B(F(0), |F'(0)|)\subseteq F(B(0,1))$, then $F(z)= F(0) + F'(0)z$.

Finding analyticity

Complex inequalities and constants

Mapping the region $\Gamma_{z}$ using the conformal map $ \omega=\frac{-2z}{z^{2}+1}$

Analytic functions and constants: Proving $f(z)-g(z)$ is constant

An entire function bounded outside a strip which contains the reals is constant

Singularities of difference of two functions

Convergence and analyticity of functions

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