Question

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

score 1.8k · Answer 1 · 2026-04-14 23:08:39

1.8k

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

Published on 14 Apr 2026 - 23:08

score 230 · Answer 2 · 2026-04-10 22:45:56

230

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Entire function satisfying an iteration formula

Published on 10 Apr 2026 - 22:45

score 87 · Answer 3 · 2026-04-16 09:21:03

87

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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 16 Apr 2026 - 9:21

score 77 · Answer 4 · 2026-04-14 17:12:09

77

Views

Find the entire function $f$.

Published on 14 Apr 2026 - 17:12

score 123 · Answer 5 · 2026-04-13 15:49:42

123

Views

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

Published on 13 Apr 2026 - 15:49

score 961 · Answer 6 · 2026-04-12 22:27:07

961

Views

Unable use countability argument in following problem

Published on 12 Apr 2026 - 22:27

score 159 · Answer 7 · 2026-04-12 00:44:40

159

Views

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

Published on 12 Apr 2026 - 0:44

score 759 · Answer 8 · 2026-04-15 03:58:59

759

Views

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

Published on 15 Apr 2026 - 3:58

score 69 · Answer 9 · 2026-04-16 14:49:50

69

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 16 Apr 2026 - 14:49

score 92 · Answer 10 · 2026-04-11 16:35:27

92

Views

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

Published on 11 Apr 2026 - 16:35

score 283 · Answer 11 · 2026-05-10 19:46:06

283

Views

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

Published on 10 May 2026 - 19:46

score 347 · Answer 12 · 2026-04-16 01:13:58

347

Views

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

Published on 16 Apr 2026 - 1:13

score 841 · Answer 13 · 2026-05-10 17:02:41

841

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 10 May 2026 - 17:02

score 808 · Answer 14 · 2026-05-10 15:52:35

808

Views

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

Published on 10 May 2026 - 15:52

score 112 · Answer 15 · 2026-04-15 16:59:27

112

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 15 Apr 2026 - 16:59

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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