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Weierstrass-type factorization (reconstruction) of a function with branch cuts

score 46 · Answer 1 · 2026-03-25 03:18:52

46

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Weierstrass-type factorization (reconstruction) of a function with branch cuts

Published on 25 Mar 2026 - 3:18

score 82 · Answer 2 · 2020-05-11 10:26:40

82

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Is this a novel factorization theorem? Solving $\sin^2(\pi x)+\sin^2\left(\frac{\pi p}{x}\right)=0$ for $x$ gives the integer factors of $p$.

Published on 11 May 2020 - 10:26

score 109 · Answer 3 · 2020-06-07 12:34:53

109

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Function on $\mathbb{C}$ with all primes as zeros?

Published on 07 Jun 2020 - 12:34

score 182 · Answer 4 · 2020-07-26 14:13:15

182

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Zeroes of a non-zero entire function

Published on 26 Jul 2020 - 14:13

score 45 · Answer 5 · 2016-10-07 12:07:20

45

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Weierstrass equation help needed

Published on 07 Oct 2016 - 12:07

score 1.5k · Answer 6 · 2016-10-26 04:21:33

1.5k

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:Duplicate: How to prove that $\cos (\pi * z) = \prod_{n \in \mathbb{Z}_{\text{odd}}} (1-\frac{2 z}{n})e^{2z/n}$

Published on 26 Oct 2016 - 4:21

score 2.1k · Answer 7 · 2017-01-15 15:59:00

2.1k

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Elementary factors in the Weierstrass Factorization Theorem

Published on 15 Jan 2017 - 15:59

score 75 · Answer 8 · 2017-01-25 17:53:25

75

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Understanding Elstrodt's proof of the $\eta$ transformation formula using the Weierstrass $\zeta$ function

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score 36 · Answer 9 · 2023-03-26 19:47:25

36

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An entire function that only has simple zeroes at the positive squares

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score 50 · Answer 10 · 2023-03-28 08:34:45

50

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Ash - Complex Variables - Sufficient conditions for the absolute and uniform convergence of the infinite product of functions

Published on 28 Mar 2023 - 8:34

score 42 · Answer 11 · 2023-05-03 08:47:19

42

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Use Weierstrass Factorization Theorem to prove $\sinh \pi z=\pi z \prod_{n=1}^{\infty}(1+\frac{z^2}{n^2})$

Published on 03 May 2023 - 8:47

score 57 · Answer 12 · 2023-05-08 17:45:15

57

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A special continuous function derived from a sum of abs sin waves

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score 49 · Answer 13 · 2023-05-13 11:52:55

49

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score 59 · Answer 14 · 2023-05-15 07:56:58

59

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How do I "stabilize" the interpolator that uses the roots?

Published on 15 May 2023 - 7:56

score 53 · Answer 15 · 2023-05-30 06:42:26

53

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Reducing polynomial from Weierstrass substitution from n-degree to n/2-degree

Published on 30 May 2023 - 6:42

List Question

Weierstrass-type factorization (reconstruction) of a function with branch cuts

Is this a novel factorization theorem? Solving $\sin^2(\pi x)+\sin^2\left(\frac{\pi p}{x}\right)=0$ for $x$ gives the integer factors of $p$.

Function on $\mathbb{C}$ with all primes as zeros?

Zeroes of a non-zero entire function

Weierstrass equation help needed

:Duplicate: How to prove that $\cos (\pi * z) = \prod_{n \in \mathbb{Z}_{\text{odd}}} (1-\frac{2 z}{n})e^{2z/n}$

Elementary factors in the Weierstrass Factorization Theorem

Understanding Elstrodt's proof of the $\eta$ transformation formula using the Weierstrass $\zeta$ function

An entire function that only has simple zeroes at the positive squares

Ash - Complex Variables - Sufficient conditions for the absolute and uniform convergence of the infinite product of functions

Use Weierstrass Factorization Theorem to prove $\sinh \pi z=\pi z \prod_{n=1}^{\infty}(1+\frac{z^2}{n^2})$

A special continuous function derived from a sum of abs sin waves

Polynomial or wave through aligned points

How do I "stabilize" the interpolator that uses the roots?

Reducing polynomial from Weierstrass substitution from n-degree to n/2-degree

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