Question

Constructing an entire function $f(z)$ such that $f(0)=1$ and $f(n^{1/3}-n^{1/6})=0$ for every $n\geq 2$

score 39 · Answer 1 · 2024-02-12 00:00:44

39

Views

Constructing an entire function $f(z)$ such that $f(0)=1$ and $f(n^{1/3}-n^{1/6})=0$ for every $n\geq 2$

Published on 12 Feb 2024 - 0:00

score 313 · Answer 2 · 2015-07-13 03:16:43

313

Views

Weierstrass factorization theorem and primality function

Published on 13 Jul 2015 - 3:16

score 97 · Answer 3 · 2015-08-20 04:22:25

97

Views

Factorization of a polynomials in complex number.

Published on 20 Aug 2015 - 4:22

score 269 · Answer 4 · 2015-09-17 17:46:13

269

Views

Weierstrass Product of $z\cos(z)-\sin(z)$

Published on 17 Sep 2015 - 17:46

score 47 · Answer 5 · 2015-09-21 22:24:30

47

Views

When is $a(z) = b(c(z)) $?

Published on 21 Sep 2015 - 22:24

score 7.8k · Answer 6 · 2016-05-30 11:59:44

7.8k

Views

Detailed explanation of the Γ reflection formula understandable by an AP Calculus student

Published on 30 May 2016 - 11:59

score 44 · Answer 7 · 2016-06-24 20:27:20

44

Views

Elliptic curve, different forms of.

Published on 24 Jun 2016 - 20:27

score 329 · Answer 8 · 2017-04-12 03:56:27

329

Views

$\{a_n\} \subseteq \mathbb C$ discrete set with no limit point . For any sequence $\{z_n\} $ , there is entire $f $ on $\mathbb C$ with $f(a_n)=z_n$?

Published on 12 Apr 2017 - 3:56

score 49 · Answer 9 · 2017-04-23 06:30:00

49

Views

$E,F$ disjoint subsets of $D$ having no limit point in $D$ ; to show a meromorphic function with poles exactly in $E$ and zeros exactly in $F$

Published on 23 Apr 2017 - 6:30

score 342 · Answer 10 · 2017-12-25 02:22:07

342

Views

Constructing a holomorphic function with a given zero set.

Published on 25 Dec 2017 - 2:22

score 47 · Answer 11 · 2020-08-27 10:21:20

47

Views

Can we do Weierstrass factorization for trigonometric substitutions? If so, in which cases?

Published on 27 Aug 2020 - 10:21

score 120 · Answer 12 · 2020-11-19 15:01:11

120

Views

How I prove absolute convergence of this infinite product?

Published on 19 Nov 2020 - 15:01

score 177 · Answer 13 · 2020-12-14 11:22:58

177

Views

Is there a closed-form expression for $\prod_{n=1}^{\infty}(1-\frac{x}{n^3})$?

Published on 14 Dec 2020 - 11:22

score 51 · Answer 14 · 2021-04-24 21:04:06

51

Views

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Published on 24 Apr 2021 - 21:04

score 330 · Answer 15 · 2021-04-26 16:44:35

330

Views

Converting equation into short Weierstrass form

Published on 26 Apr 2021 - 16:44

List Question

Constructing an entire function $f(z)$ such that $f(0)=1$ and $f(n^{1/3}-n^{1/6})=0$ for every $n\geq 2$

Weierstrass factorization theorem and primality function

Factorization of a polynomials in complex number.

Weierstrass Product of $z\cos(z)-\sin(z)$

When is $a(z) = b(c(z)) $?

Detailed explanation of the Γ reflection formula understandable by an AP Calculus student

Elliptic curve, different forms of.

$\{a_n\} \subseteq \mathbb C$ discrete set with no limit point . For any sequence $\{z_n\} $ , there is entire $f $ on $\mathbb C$ with $f(a_n)=z_n$?

$E,F$ disjoint subsets of $D$ having no limit point in $D$ ; to show a meromorphic function with poles exactly in $E$ and zeros exactly in $F$

Constructing a holomorphic function with a given zero set.

Can we do Weierstrass factorization for trigonometric substitutions? If so, in which cases?

How I prove absolute convergence of this infinite product?

Is there a closed-form expression for $\prod_{n=1}^{\infty}(1-\frac{x}{n^3})$?

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Converting equation into short Weierstrass form

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