Question

Zeros of $e^{z}-z$, Stein-Shakarchi Complex Analysis Chapter 5, Exercise 13

score 1.5k · Answer 1 · 2014-01-30 13:05:52

1.5k

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Zeros of $e^{z}-z$, Stein-Shakarchi Complex Analysis Chapter 5, Exercise 13

Published on 30 Jan 2014 - 13:05

score 1.1k · Answer 2 · 2014-02-04 10:42:03

1.1k

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$F$ entire with $\lim_{k \rightarrow \infty} F(z + N_{k}) = h(z)$ for every $h$ entire

Published on 04 Feb 2014 - 10:42

score 496 · Answer 3 · 2017-04-11 19:16:12

496

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Holomorphic $f$ and $g$ such that $e^{f(z)}+e^{g(z)}=1$ on $\mathbb C$

Published on 11 Apr 2017 - 19:16

score 241 · Answer 4 · 2017-04-12 01:20:39

241

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polynomial in entire function with polynomial coefficients

Published on 12 Apr 2017 - 1:20

score 330 · Answer 5 · 2026-03-25 09:29:02

330

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$\{a_n\} \subseteq \mathbb C$ discrete set with no limit point . For any sequence $\{z_n\} $ , there is entire $f $ on $\mathbb C$ with $f(a_n)=z_n$?

Published on 25 Mar 2026 - 9:29

score 114 · Answer 6 · 2017-04-14 21:58:54

114

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Entire functions problem

Published on 14 Apr 2017 - 21:58

score 126 · Answer 7 · 2017-04-18 02:42:06

126

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Showing the following function is entire.

Published on 18 Apr 2017 - 2:42

score 1k · Answer 8 · 2017-05-04 03:35:53

1k

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Let $f$ entire funtion such that $\left|f(z)\right|=1$ when $|z|=1$. Then $f(z)=Cz^{m}$ for some $m\in \mathbb{N}$ and $C\in\mathbb{C}$ with $|C|=1$.

Published on 04 May 2017 - 3:35

score 637 · Answer 9 · 2017-05-04 18:17:18

637

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construct entire function

Published on 04 May 2017 - 18:17

score 345 · Answer 10 · 2017-05-17 17:41:25

345

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Sequence of uniformly converging entire function is equivalent to its limit for sufficiently large $n$ given $f_n(z)=f(z)=0$

Published on 17 May 2017 - 17:41

score 310 · Answer 11 · 2017-05-18 22:41:19

310

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The composition of non-linear entire functions with no fixed points has infinitely many fixed points.

Published on 18 May 2017 - 22:41

score 83 · Answer 12 · 2017-05-22 12:39:35

83

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Entire functions of several complex variables with the same modulus

Published on 22 May 2017 - 12:39

score 511 · Answer 13 · 2017-05-22 22:08:23

511

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Computing $\sum_{n=0}^\infty \frac{(-1)^n}{2n+1} $

Published on 22 May 2017 - 22:08

score 48 · Answer 14 · 2017-05-25 06:04:26

48

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Entire solutions of first order linear homogeneous evolution PDEs

Published on 25 May 2017 - 6:04

score 473 · Answer 15 · 2017-05-25 16:27:55

473

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Αn entire function as an infinite sum of entire functions

Published on 25 May 2017 - 16:27

List Question

Zeros of $e^{z}-z$, Stein-Shakarchi Complex Analysis Chapter 5, Exercise 13

$F$ entire with $\lim_{k \rightarrow \infty} F(z + N_{k}) = h(z)$ for every $h$ entire

Holomorphic $f$ and $g$ such that $e^{f(z)}+e^{g(z)}=1$ on $\mathbb C$

polynomial in entire function with polynomial coefficients

$\{a_n\} \subseteq \mathbb C$ discrete set with no limit point . For any sequence $\{z_n\} $ , there is entire $f $ on $\mathbb C$ with $f(a_n)=z_n$?

Entire functions problem

Showing the following function is entire.

Let $f$ entire funtion such that $\left|f(z)\right|=1$ when $|z|=1$. Then $f(z)=Cz^{m}$ for some $m\in \mathbb{N}$ and $C\in\mathbb{C}$ with $|C|=1$.

construct entire function

Sequence of uniformly converging entire function is equivalent to its limit for sufficiently large $n$ given $f_n(z)=f(z)=0$

The composition of non-linear entire functions with no fixed points has infinitely many fixed points.

Entire functions of several complex variables with the same modulus

Computing $\sum_{n=0}^\infty \frac{(-1)^n}{2n+1} $

Entire solutions of first order linear homogeneous evolution PDEs

Αn entire function as an infinite sum of entire functions

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