Question

f is analytic except possibly on $|z|=1$ and agrees with entire function $g$ when $|z|=1$, then $f$ is entire.

score 361 · Answer 1 · 2026-03-25 23:39:36

361

Views

f is analytic except possibly on $|z|=1$ and agrees with entire function $g$ when $|z|=1$, then $f$ is entire.

Published on 25 Mar 2026 - 23:39

score 217 · Answer 2 · 2020-07-09 00:56:32

217

Views

Conditions on an entire function that would make it a polynomial

Published on 09 Jul 2020 - 0:56

score 153 · Answer 3 · 2020-07-24 06:37:00

153

Views

Let $f$ be an entire function. And assume $f(z)$ is real on $Im(z)=0$ and $Im(z)=\pi$ lines. Show $f$ is $2\pi i$ periodic.

Published on 24 Jul 2020 - 6:37

score 65 · Answer 4 · 2016-07-18 05:46:59

65

Views

Uniformity of Analytic Function Growth Order

Published on 18 Jul 2016 - 5:46

score 349 · Answer 5 · 2016-07-31 17:23:17

349

Views

Entire function with zeros only at the natural numbers

Published on 31 Jul 2016 - 17:23

score 3.5k · Answer 6 · 2016-08-04 00:43:10

3.5k

Views

State why the function $f(z)=2z^2-3-ze^z+e^{-z}$ is entire

Published on 04 Aug 2016 - 0:43

score 115 · Answer 7 · 2016-08-07 18:43:07

115

Views

Show that a given function is entire

Published on 07 Aug 2016 - 18:43

score 172 · Answer 8 · 2016-08-24 14:28:59

172

Views

Which entire functions $h(z)$ can be written as $h(z)=f(z+1)-f(z)$ for some entire function $f$?

Published on 24 Aug 2016 - 14:28

score 2.1k · Answer 9 · 2016-09-01 03:59:37

2.1k

Views

Given entire function has infinitely many zeros

Published on 01 Sep 2016 - 3:59

score 222 · Answer 10 · 2016-09-14 00:25:14

222

Views

Question about entire functions and Liouville's Theorem

Published on 14 Sep 2016 - 0:25

score 161 · Answer 11 · 2016-09-20 07:46:04

even entire function of exponential type and bounded on the real axis implies that it has infinite complex roots;

score 177 · Answer 12 · 2016-09-23 21:18:05

177

Views

How do I overcome with the numerical issue?

Published on 23 Sep 2016 - 21:18

score 357 · Answer 13 · 2016-09-26 20:43:24

357

Views

Proving $g(z)=z^{2z}\sin{z}$ is not an entire function

Published on 26 Sep 2016 - 20:43

score 267 · Answer 14 · 2016-10-08 17:32:07

267

Views

Show that $f^{n}(0)=0$ for infinitely many $n\ge 0$.

Published on 08 Oct 2016 - 17:32

score 85 · Answer 15 · 2016-10-10 15:08:16

85

Views

How to prove the following inequalities

Published on 10 Oct 2016 - 15:08

List Question

f is analytic except possibly on $|z|=1$ and agrees with entire function $g$ when $|z|=1$, then $f$ is entire.

Conditions on an entire function that would make it a polynomial

Let $f$ be an entire function. And assume $f(z)$ is real on $Im(z)=0$ and $Im(z)=\pi$ lines. Show $f$ is $2\pi i$ periodic.

Uniformity of Analytic Function Growth Order

Entire function with zeros only at the natural numbers

State why the function $f(z)=2z^2-3-ze^z+e^{-z}$ is entire

Show that a given function is entire

Which entire functions $h(z)$ can be written as $h(z)=f(z+1)-f(z)$ for some entire function $f$?

Given entire function has infinitely many zeros

Question about entire functions and Liouville's Theorem

even entire function of exponential type and bounded on the real axis implies that it has infinite complex roots;

How do I overcome with the numerical issue?

Proving $g(z)=z^{2z}\sin{z}$ is not an entire function

Show that $f^{n}(0)=0$ for infinitely many $n\ge 0$.

How to prove the following inequalities

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