Question

Examples of entire functions $f(z)$ with the property $\lim\limits_{x\rightarrow \infty}|f(x+iy)|=\begin{cases} 0,& y\neq 0\\ M,& y=0 \end{cases}$

score 424 · Answer 1 · 2018-01-11 14:46:48

424

Views

Examples of entire functions $f(z)$ with the property $\lim\limits_{x\rightarrow \infty}|f(x+iy)|=\begin{cases} 0,& y\neq 0\\ M,& y=0 \end{cases}$

Published on 11 Jan 2018 - 14:46

score 586 · Answer 2 · 2011-04-18 19:57:20

586

Views

Finding an entire function such that $|f(z)| > e^{Im f(z)}$ and $f(0)=2$ & an analytic function that has an essential singularity at $z=0$

Published on 18 Apr 2011 - 19:57

score 477 · Answer 3 · 2011-04-19 18:40:32

477

Views

How to find an entire function $f(z)$ such that $f(n) = \sqrt {|n|}$ for every integer $n$?

Published on 19 Apr 2011 - 18:40

score 8.6k · Answer 4 · 2011-05-04 00:12:42

8.6k

Views

How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?

Published on 04 May 2011 - 0:12

score 662 · Answer 5 · 2012-10-10 22:34:51

662

Views

Is an infinite product of entire functions: $\prod\limits_{n=1}^{\infty}f_{n}(z)$, a entire function?

Published on 10 Oct 2012 - 22:34

score 2.7k · Answer 6 · 2013-01-09 19:51:29

2.7k

Views

Order of growth of the entire function $\sin(\sqrt{z})/\sqrt{z}$

Published on 09 Jan 2013 - 19:51

score 53 · Answer 7 · 2020-07-31 12:06:12

53

Views

A deduction in 1st course of complex analysis if a particular series is given absolutely

Published on 31 Jul 2020 - 12:06

score 42 · Answer 8 · 2020-07-31 16:40:41

42

Views

A question based on analyticity of entire functions

Published on 31 Jul 2020 - 16:40

score 171 · Answer 9 · 2020-08-01 14:02:06

171

Views

prove that if $|f(z)|\geq |z|+|\sin(z)|$ then it cannot be an entire function

Published on 01 Aug 2020 - 14:02

score 452 · Answer 10 · 2020-08-07 15:29:44

452

Views

Is an entire function "determined by" its maximum modulus on each circle centered at the origin?

Published on 07 Aug 2020 - 15:29

score 89 · Answer 11 · 2020-08-09 16:43:07

89

Views

if a series of polynomial converge uniformally locally, and each of then has only real roots, then if f is an entire, then has only real roots.

Published on 09 Aug 2020 - 16:43

score 70 · Answer 12 · 2020-08-12 16:23:22

70

Views

An entire function satisfying $Im(f(z)) > 0$ for all $z \in \mathbb{C}$ is constant

Published on 12 Aug 2020 - 16:23

score 656 · Answer 13 · 2020-08-18 15:53:24

656

Views

If $g(z) = f(1/z)$ and $g$ has a pole at $0$ and $f$ entire.Then there is a $z_0$ such that $f(z_0) = 0$.

Published on 18 Aug 2020 - 15:53

score 178 · Answer 14 · 2020-08-20 18:10:45

178

Views

Davenport's proof of the Hadamard theorem

Published on 20 Aug 2020 - 18:10

score 242 · Answer 15 · 2020-09-01 08:31:26

242

Views

True or false? If $f$ and $g$ are entire functions such that $f(z) g(z) =1$ for all $z$, then $f$ and $g$ are constants

Published on 01 Sep 2020 - 8:31

List Question

Examples of entire functions $f(z)$ with the property $\lim\limits_{x\rightarrow \infty}|f(x+iy)|=\begin{cases} 0,& y\neq 0\\ M,& y=0 \end{cases}$

Finding an entire function such that $|f(z)| > e^{Im f(z)}$ and $f(0)=2$ & an analytic function that has an essential singularity at $z=0$

How to find an entire function $f(z)$ such that $f(n) = \sqrt {|n|}$ for every integer $n$?

How to Prove that if $f(z)$ is entire, and $f(z+i) = f(z), f(z+1) = f(z)$, then $f(z)$ is constant?

Is an infinite product of entire functions: $\prod\limits_{n=1}^{\infty}f_{n}(z)$, a entire function?

Order of growth of the entire function $\sin(\sqrt{z})/\sqrt{z}$

A deduction in 1st course of complex analysis if a particular series is given absolutely

A question based on analyticity of entire functions

prove that if $|f(z)|\geq |z|+|\sin(z)|$ then it cannot be an entire function

Is an entire function "determined by" its maximum modulus on each circle centered at the origin?

if a series of polynomial converge uniformally locally, and each of then has only real roots, then if f is an entire, then has only real roots.

An entire function satisfying $Im(f(z)) > 0$ for all $z \in \mathbb{C}$ is constant

If $g(z) = f(1/z)$ and $g$ has a pole at $0$ and $f$ entire.Then there is a $z_0$ such that $f(z_0) = 0$.

Davenport's proof of the Hadamard theorem

True or false? If $f$ and $g$ are entire functions such that $f(z) g(z) =1$ for all $z$, then $f$ and $g$ are constants

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