Question

Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”

score 658 · Answer 1 · 2021-05-30 04:31:48

Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”

Published on 30 May 2021 - 4:31

score 91 · Answer 2 · 2021-05-31 03:00:23

Why doesn't $f(z)=\sqrt z$ work as a counterexample to If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ cannot be an entire function.

score 293 · Answer 3 · 2021-06-03 12:12:37

293

Views

Find all entire functions which satisfy the following condition

Published on 03 Jun 2021 - 12:12

score 167 · Answer 4 · 2021-06-04 15:14:59

167

Views

Let $f$ be a non constant holomorphic function such that $f$ is real iff $z$ is real: show that $f$ is linear.

Published on 04 Jun 2021 - 15:14

score 198 · Answer 5 · 2021-06-07 22:48:45

198

Views

Find all possible Laurent series expansion of $\frac{f(z)}{z-w}$

Published on 07 Jun 2021 - 22:48

score 213 · Answer 6 · 2021-06-12 16:03:06

213

Views

Order of an entire function less than 1 implies exponential type 0

Published on 12 Jun 2021 - 16:03

score 64 · Answer 7 · 2021-06-26 18:11:10

64

Views

Given $\omega_1,\omega_2\in\mathbb{C}$ being $\mathbb{R}$-linearly independent, find $B\in\mathbb{C}$ such that $e^{B\omega_j}=a_j$

Published on 26 Jun 2021 - 18:11

score 512 · Answer 8 · 2021-07-07 14:01:05

512

Views

Does the set of entire functions have the same cardinality as the reals?

Published on 07 Jul 2021 - 14:01

score 36 · Answer 9 · 2021-07-10 12:46:21

36

Views

Weierstrass factorisation

Published on 10 Jul 2021 - 12:46

score 168 · Answer 10 · 2021-07-14 08:08:27

168

Views

Show that $\int_1^{\infty} t^{x-1} e^{-t} dt$ is entire.

Published on 14 Jul 2021 - 8:08

score 193 · Answer 11 · 2021-07-14 16:27:38

193

Views

Which of the following functions is/are constant?

Published on 14 Jul 2021 - 16:27

score 234 · Answer 12 · 2026-03-26 14:34:25

234

Views

Order of growth of $\prod_{n=1}^{\infty}(1-a^nz)$ for $0<|a|<1$

Published on 26 Mar 2026 - 14:34

score 251 · Answer 13 · 2021-07-16 20:25:10

251

Views

$\lim_{\vert z\vert\to\infty}\frac{zf'(z)}{f(z)}=n\in\mathbb{N}$ implies $f$ is a polynomial

Published on 16 Jul 2021 - 20:25

score 92 · Answer 14 · 2021-07-29 11:15:50

92

Views

If $f$ is an non-null entire function that satisfies $|f(z)|=2$ for all $z\in\partial \Bbb D$, then $f$ is constant?

Published on 29 Jul 2021 - 11:15

score 60 · Answer 15 · 2021-08-10 00:59:03

60

Views

Do Meromorphic Functions automatically give us Entire Functions?

Published on 10 Aug 2021 - 0:59

List Question

Disproving the statement "If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ is not entire.”

Why doesn't $f(z)=\sqrt z$ work as a counterexample to If $f(z)$ is not an entire function, then $g(z) = f^2(z)$ cannot be an entire function.

Find all entire functions which satisfy the following condition

Let $f$ be a non constant holomorphic function such that $f$ is real iff $z$ is real: show that $f$ is linear.

Find all possible Laurent series expansion of $\frac{f(z)}{z-w}$

Order of an entire function less than 1 implies exponential type 0

Given $\omega_1,\omega_2\in\mathbb{C}$ being $\mathbb{R}$-linearly independent, find $B\in\mathbb{C}$ such that $e^{B\omega_j}=a_j$

Does the set of entire functions have the same cardinality as the reals?

Weierstrass factorisation

Show that $\int_1^{\infty} t^{x-1} e^{-t} dt$ is entire.

Which of the following functions is/are constant?

Order of growth of $\prod_{n=1}^{\infty}(1-a^nz)$ for $0<|a|<1$

$\lim_{\vert z\vert\to\infty}\frac{zf'(z)}{f(z)}=n\in\mathbb{N}$ implies $f$ is a polynomial

If $f$ is an non-null entire function that satisfies $|f(z)|=2$ for all $z\in\partial \Bbb D$, then $f$ is constant?

Do Meromorphic Functions automatically give us Entire Functions?

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