Question

$f$ entire function with $|f(z)| \leq 1 + |\Im z|$, is $f$ constant?

score 214 · Answer 1 · 2019-08-09 17:27:10

214

Views

$f$ entire function with $|f(z)| \leq 1 + |\Im z|$, is $f$ constant?

Published on 09 Aug 2019 - 17:27

score 130 · Answer 2 · 2019-08-17 18:07:27

130

Views

Entire function such that $\text{Im}f = \text{Re} ^4 f + 1$ is constant

Published on 17 Aug 2019 - 18:07

score 425 · Answer 3 · 2026-03-25 12:53:51

425

Views

An entire function satisfies $f(az+b)=f(z)$

Published on 25 Mar 2026 - 12:53

score 62 · Answer 4 · 2019-08-18 22:15:24

62

Views

Complex analysis question on conformal mappings

Published on 18 Aug 2019 - 22:15

score 125 · Answer 5 · 2019-08-31 11:50:09

125

Views

Find all analytic functions satisfying the following condition

Published on 31 Aug 2019 - 11:50

score 226 · Answer 6 · 2019-09-12 06:36:37

226

Views

An application of the Paley-Wiener theorem

Published on 12 Sep 2019 - 6:36

score 1.4k · Answer 7 · 2019-09-22 12:52:12

1.4k

Views

find all entire functions $f$ such that $f(\frac{1}{n})=f(\frac{1}{n²})$

Published on 22 Sep 2019 - 12:52

score 102 · Answer 8 · 2019-09-22 15:00:58

102

Views

find entire functions such that $f( e^\frac{1}{n})=\frac{n+1}{n}$ for all $n\in \mathbb{N}$

Published on 22 Sep 2019 - 15:00

score 54 · Answer 9 · 2019-09-24 15:56:31

54

Views

$f$ is an entire function if $|f(z)|\geq e^\pi $, what can we say about $f$

Published on 24 Sep 2019 - 15:56

score 165 · Answer 10 · 2019-09-29 14:09:06

165

Views

All entire functions $f(z)$ such that 0 is removable singularity of $f(1/z)$?

Published on 29 Sep 2019 - 14:09

score 338 · Answer 11 · 2014-05-14 20:40:44

338

Views

Let $G(z)=\prod\limits_{n=1}^{\infty}\left(1+\frac z n\right)e^{-\frac z n}$. Show that it's an entire function and $G(z-1)=ze^{\gamma}G(z)$

Published on 14 May 2014 - 20:40

score 259 · Answer 12 · 2019-10-06 12:01:31

259

Views

Is there an entire function with $f(n) = f(-n) = \frac1{n^2}$?

Published on 06 Oct 2019 - 12:01

score 135 · Answer 13 · 2019-10-07 07:42:55

135

Views

Prove that no such $f$ exists

Published on 07 Oct 2019 - 7:42

score 67 · Answer 14 · 2019-10-16 21:10:18

67

Views

Show that $u(x,y)$ is a constant function

Published on 16 Oct 2019 - 21:10

score 51 · Answer 15 · 2019-10-21 19:14:18

51

Views

Determining Jensen's Polynomial for $k$ and $k+1$

Published on 21 Oct 2019 - 19:14

List Question

$f$ entire function with $|f(z)| \leq 1 + |\Im z|$, is $f$ constant?

Entire function such that $\text{Im}f = \text{Re} ^4 f + 1$ is constant

An entire function satisfies $f(az+b)=f(z)$

Complex analysis question on conformal mappings

Find all analytic functions satisfying the following condition

An application of the Paley-Wiener theorem

find all entire functions $f$ such that $f(\frac{1}{n})=f(\frac{1}{n²})$

find entire functions such that $f( e^\frac{1}{n})=\frac{n+1}{n}$ for all $n\in \mathbb{N}$

$f$ is an entire function if $|f(z)|\geq e^\pi $, what can we say about $f$

All entire functions $f(z)$ such that 0 is removable singularity of $f(1/z)$?

Let $G(z)=\prod\limits_{n=1}^{\infty}\left(1+\frac z n\right)e^{-\frac z n}$. Show that it's an entire function and $G(z-1)=ze^{\gamma}G(z)$

Is there an entire function with $f(n) = f(-n) = \frac1{n^2}$?

Prove that no such $f$ exists

Show that $u(x,y)$ is a constant function

Determining Jensen's Polynomial for $k$ and $k+1$

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