Question

Finding an equality of entire funcitons using Local Cauchy properties.

score 29 · Answer 1 · 2020-04-24 15:30:37

29

Views

Finding an equality of entire funcitons using Local Cauchy properties.

Published on 24 Apr 2020 - 15:30

score 85 · Answer 2 · 2020-04-24 17:15:52

85

Views

Give an example of unbounded and entire function on $\mathbb{C}$ such that its restriction on $\mathbb{R}$ is real valued bounded function. Justify

Published on 24 Apr 2020 - 17:15

score 605 · Answer 3 · 2026-03-25 09:32:02

605

Views

Suppose that an entire function $f$ is holomorphic at infinity. Show that $f$ is constant.

Published on 25 Mar 2026 - 9:32

score 218 · Answer 4 · 2026-03-25 16:00:04

218

Views

Hartog's Theorem and Entire Functions

Published on 25 Mar 2026 - 16:00

score 239 · Answer 5 · 2020-05-03 16:50:40

If $f(z)=\sum a_nz^n$ is an entire function of finite order, then $|a_n|\leq (\frac{e\lambda}{n})^{n/\lambda}$ holds for all large enough $n$.

score 4k · Answer 6 · 2020-05-04 04:04:23

4k

Views

If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.

Published on 04 May 2020 - 4:04

score 103 · Answer 7 · 2020-05-04 15:07:19

103

Views

Find entire $f$ from $|f|$

Published on 04 May 2020 - 15:07

score 388 · Answer 8 · 2020-05-04 15:26:14

388

Views

If $f(z)=\sum c_nz^n$ is an entire function of finite genus $\mu$ then $\lim_{n\to\infty}c_n(n!)^{1/(\mu+1)}=0$

Published on 04 May 2020 - 15:26

score 2.3k · Answer 9 · 2020-05-09 09:04:22

2.3k

Views

Prove that if $f$ is an entire function with $\lim_{z \to \infty}|f(z)| = \infty$, then $f$ has at least one zero.

Published on 09 May 2020 - 9:04

score 119 · Answer 10 · 2020-05-10 07:58:17

119

Views

Zeros of the equation $e^z-z$ in the complex plane

Published on 10 May 2020 - 7:58

score 586 · Answer 11 · 2020-05-15 03:47:38

586

Views

Is $e^{\sqrt{z}}$ an entire function?

Published on 15 May 2020 - 3:47

score 108 · Answer 12 · 2020-05-19 16:23:36

108

Views

Entire functions with infinitely many zeros

Published on 19 May 2020 - 16:23

score 98 · Answer 13 · 2020-05-22 12:45:00

98

Views

Liouville's theorem question - show f is constant

Published on 22 May 2020 - 12:45

score 46 · Answer 14 · 2020-05-23 10:50:54

46

Views

$e^{-z^2}$ cannot be expressed as $\int_1^{-1} f(t)e^{itz}dt$ for some $f\in L^1[-1,1]$

Published on 23 May 2020 - 10:50

score 97 · Answer 15 · 2020-05-24 18:22:19

97

Views

Bound on integral on function implies bound order of entire function

Published on 24 May 2020 - 18:22

List Question

Finding an equality of entire funcitons using Local Cauchy properties.

Give an example of unbounded and entire function on $\mathbb{C}$ such that its restriction on $\mathbb{R}$ is real valued bounded function. Justify

Suppose that an entire function $f$ is holomorphic at infinity. Show that $f$ is constant.

Hartog's Theorem and Entire Functions

If $f(z)=\sum a_nz^n$ is an entire function of finite order, then $|a_n|\leq (\frac{e\lambda}{n})^{n/\lambda}$ holds for all large enough $n$.

If $f$ is a nonconstant entire function such that $|f(z)|\geq M|z|^n$ for $|z|\geq R$, then $f$ is a polynomial of degree atleast $n$.

Find entire $f$ from $|f|$

If $f(z)=\sum c_nz^n$ is an entire function of finite genus $\mu$ then $\lim_{n\to\infty}c_n(n!)^{1/(\mu+1)}=0$

Prove that if $f$ is an entire function with $\lim_{z \to \infty}|f(z)| = \infty$, then $f$ has at least one zero.

Zeros of the equation $e^z-z$ in the complex plane

Is $e^{\sqrt{z}}$ an entire function?

Entire functions with infinitely many zeros

Liouville's theorem question - show f is constant

$e^{-z^2}$ cannot be expressed as $\int_1^{-1} f(t)e^{itz}dt$ for some $f\in L^1[-1,1]$

Bound on integral on function implies bound order of entire function

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