Question

Order of the entire function $f(z)=\sin(z)$

score 1.7k · Answer 1 · 2018-08-28 15:40:08

1.7k

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Order of the entire function $f(z)=\sin(z)$

Published on 28 Aug 2018 - 15:40

score 227 · Answer 2 · 2018-08-29 20:21:50

227

Views

Entire function satisfying an iteration formula

Published on 29 Aug 2018 - 20:21

score 84 · Answer 3 · 2018-09-06 17:33:15

84

Views

Let $f$ be an entire function such that image of $f$ lies in $L=\{2+iy:y\in R\}$ if $f(2+i)=2+i$ then show that $f(z)=2+i$ for all $z \in C$

Published on 06 Sep 2018 - 17:33

score 73 · Answer 4 · 2018-09-16 09:10:35

73

Views

Find the entire function $f$.

Published on 16 Sep 2018 - 9:10

score 120 · Answer 5 · 2018-09-17 08:32:30

120

Views

Example of entire function on $\mathbb C$ such that which does not take only one value in $\mathbb C$

Published on 17 Sep 2018 - 8:32

score 958 · Answer 6 · 2018-09-17 08:48:12

958

Views

Unable use countability argument in following problem

Published on 17 Sep 2018 - 8:48

score 156 · Answer 7 · 2018-09-17 17:14:31

156

Views

Example of entire function which can take every value except .....

Published on 17 Sep 2018 - 17:14

score 756 · Answer 8 · 2018-09-21 05:49:19

756

Views

If $f$ is entire and $f(z)\to \infty$, for $z\to \infty$ , then $f(z)$ is polynomial

Published on 21 Sep 2018 - 5:49

score 66 · Answer 9 · 2018-09-27 12:06:11

66

Views

Given $g\in L^1(-a,a)$ and $f(x+iy):=\int_{-a}^ag(t)e^{2\pi i(x+iy)t}dt$, is it true that $|f(z)|=o(e^{2\pi a|z|}), z\rightarrow \infty$?

Published on 27 Sep 2018 - 12:06

score 89 · Answer 10 · 2018-10-15 16:47:47

89

Views

Solving functional equation $\sin f = f^2-3if+\pi$

Published on 15 Oct 2018 - 16:47

score 281 · Answer 11 · 2026-03-24 15:46:38

281

Views

How to show an entire function bounded from above is identically zero

Published on 24 Mar 2026 - 15:46

score 344 · Answer 12 · 2018-11-04 17:23:19

344

Views

Take $f$ and entire function such that $f(z) = f(z+1)=f(z+\sqrt{2})$, then it is constant

Published on 04 Nov 2018 - 17:23

score 838 · Answer 13 · 2026-03-25 07:46:31

838

Views

Use maximum modules principle to prove that if $\sup_{|z| = R}|f(z)|\leq AR^{k} + B$ with $f$ entire, then $f$ is a polynomial

Published on 25 Mar 2026 - 7:46

score 807 · Answer 14 · 2026-03-25 01:29:07

807

Views

If $f$ is an entire function with $|\,f(z)|\le|\operatorname{Re}(z)|$, then $\,f\equiv 0$.

Published on 25 Mar 2026 - 1:29

score 109 · Answer 15 · 2026-02-23 02:50:26

109

Views

Does there exist a nonconstant entire function with $f^{(n)}(0)=3^n$ for $n$ even and $f^{(n)}(0)=(n-1)!$ for $n$ odd?

Published on 23 Feb 2026 - 2:50

List Question

Order of the entire function $f(z)=\sin(z)$

Entire function satisfying an iteration formula

Let $f$ be an entire function such that image of $f$ lies in $L=\{2+iy:y\in R\}$ if $f(2+i)=2+i$ then show that $f(z)=2+i$ for all $z \in C$

Find the entire function $f$.

Example of entire function on $\mathbb C$ such that which does not take only one value in $\mathbb C$

Unable use countability argument in following problem

Example of entire function which can take every value except .....

If $f$ is entire and $f(z)\to \infty$, for $z\to \infty$ , then $f(z)$ is polynomial

Given $g\in L^1(-a,a)$ and $f(x+iy):=\int_{-a}^ag(t)e^{2\pi i(x+iy)t}dt$, is it true that $|f(z)|=o(e^{2\pi a|z|}), z\rightarrow \infty$?

Solving functional equation $\sin f = f^2-3if+\pi$

How to show an entire function bounded from above is identically zero

Take $f$ and entire function such that $f(z) = f(z+1)=f(z+\sqrt{2})$, then it is constant

Use maximum modules principle to prove that if $\sup_{|z| = R}|f(z)|\leq AR^{k} + B$ with $f$ entire, then $f$ is a polynomial

If $f$ is an entire function with $|\,f(z)|\le|\operatorname{Re}(z)|$, then $\,f\equiv 0$.

Does there exist a nonconstant entire function with $f^{(n)}(0)=3^n$ for $n$ even and $f^{(n)}(0)=(n-1)!$ for $n$ odd?

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