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 40 · Answer 1 · 2026-03-25 09:29:00

40

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 25 Mar 2026 - 9:29

score 314 · Answer 2 · 2026-03-25 09:22:21

314

Views

Weierstrass factorization theorem and primality function

Published on 25 Mar 2026 - 9:22

score 98 · Answer 3 · 2026-03-25 09:23:23

98

Views

Factorization of a polynomials in complex number.

Published on 25 Mar 2026 - 9:23

score 272 · Answer 4 · 2026-04-15 00:13:41

272

Views

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

Published on 15 Apr 2026 - 0:13

score 49 · Answer 5 · 2026-04-05 17:16:51

49

Views

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

Published on 05 Apr 2026 - 17:16

score 7.8k · Answer 6 · 2026-03-25 09:28:39

7.8k

Views

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

Published on 25 Mar 2026 - 9:28

score 46 · Answer 7 · 2026-04-06 02:50:52

46

Views

Elliptic curve, different forms of.

Published on 06 Apr 2026 - 2:50

score 330 · Answer 8 · 2026-03-25 09:29:02

330

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 25 Mar 2026 - 9:29

score 50 · Answer 9 · 2026-03-25 09:30:03

50

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 25 Mar 2026 - 9:30

score 343 · Answer 10 · 2026-03-25 11:08:29

343

Views

Constructing a holomorphic function with a given zero set.

Published on 25 Mar 2026 - 11:08

score 48 · Answer 11 · 2026-03-25 09:25:22

48

Views

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

Published on 25 Mar 2026 - 9:25

score 123 · Answer 12 · 2026-04-14 00:57:14

123

Views

How I prove absolute convergence of this infinite product?

Published on 14 Apr 2026 - 0:57

score 178 · Answer 13 · 2026-03-25 11:03:20

178

Views

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

Published on 25 Mar 2026 - 11:03

score 54 · Answer 14 · 2026-04-12 14:00:40

54

Views

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

Published on 12 Apr 2026 - 14:00

score 331 · Answer 15 · 2026-03-25 10:58:49

331

Views

Converting equation into short Weierstrass form

Published on 25 Mar 2026 - 10:58

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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