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How to find $f(m)=\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^m}\right)^{-1}$ (if $m>1$)?

score 151 · Answer 1 · 2026-03-17 11:56:19

151

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How to find $f(m)=\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^m}\right)^{-1}$ (if $m>1$)?

Published on 17 Mar 2026 - 11:56

score 636 · Answer 2 · 2026-03-17 06:16:54

636

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Counterexample to Cauchy product theorem

Published on 17 Mar 2026 - 6:16

score 94 · Answer 3 · 2026-03-16 22:14:58

94

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identity for finding value of $\pi$

Published on 16 Mar 2026 - 22:14

score 57 · Answer 4 · 2026-03-17 11:37:11

57

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A confusing sequence of products

Published on 17 Mar 2026 - 11:37

score 141 · Answer 5 · 2026-03-17 09:08:40

141

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Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization

Published on 17 Mar 2026 - 9:08

score 46 · Answer 6 · 2026-03-17 10:51:46

46

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How to find $(a_{1}a_{2})^n+(a_{1}a_{3})^n+(a_{2}a_{3})^n+\cdots$, which came from $\prod\limits_{k=1}^{\infty}(1-a_{k}x)$?

Published on 17 Mar 2026 - 10:51

score 77 · Answer 7 · 2026-03-17 20:40:04

77

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Derivation of $\lim_{s\to1}\zeta(s)-\log\prod_{n=1}^\infty(1+n^{-s})=\gamma$

Published on 17 Mar 2026 - 20:40

score 114 · Answer 8 · 2026-03-17 09:50:32

114

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Euler's "On transcendental progressions..." [E19]

Published on 17 Mar 2026 - 9:50

score 611 · Answer 9 · 2026-03-17 20:52:09

611

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Alternate proof for Viète's infinite product of nested radicals

Published on 17 Mar 2026 - 20:52

score 71 · Answer 10 · 2026-03-17 15:55:22

71

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Does $\prod_{k=1}^\infty 1- \frac{1}{k^\alpha}$ converge for $\alpha >1$?

Published on 17 Mar 2026 - 15:55

score 58 · Answer 11 · 2026-03-17 13:15:52

58

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Understanding the proof of $\text{Theorem (8.1.7)}$ in Greene's Function Theory of One Complex Varible?

Published on 17 Mar 2026 - 13:15

score 145 · Answer 12 · 2026-03-26 06:22:20

145

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Proving the convergence of $\bigg (\sum_{n}^{\nu} \bigg( \sum_{n}^{\chi} |\log(p_{n})+\log(q_{n})| \bigg ) \bigg )$?

Published on 26 Mar 2026 - 6:22

score 149 · Answer 13 · 2026-03-26 06:22:21

149

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Why do we have $ \ln(z) = \frac{z-1}{e -1} \prod_{n = 1}^{\infty} \frac{ \exp(2^{-n}) +1} {z^{2^{-n}} + 1} $

Published on 26 Mar 2026 - 6:22

score 213 · Answer 14 · 2026-03-26 06:21:48

213

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Derivatives of Infinite Product that Diverges to 0

Published on 26 Mar 2026 - 6:21

score 134 · Answer 15 · 2026-03-26 06:21:10

134

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Does $\prod \limits_{n=2}^{\infty }\left(1+\frac{1}{n\,\ln(n)}\right)$ converge?

Published on 26 Mar 2026 - 6:21

List Question

How to find $f(m)=\prod\limits_{n=2}^{\infty}\left(1-\frac{1}{n^m}\right)^{-1}$ (if $m>1$)?

Counterexample to Cauchy product theorem

identity for finding value of $\pi$

A confusing sequence of products

Deriving $\sin(\pi s)=\pi s\prod_{n=1}^\infty (1-\frac{s^2}{n^2})$ without Hadamard Factorization

How to find $(a_{1}a_{2})^n+(a_{1}a_{3})^n+(a_{2}a_{3})^n+\cdots$, which came from $\prod\limits_{k=1}^{\infty}(1-a_{k}x)$?

Derivation of $\lim_{s\to1}\zeta(s)-\log\prod_{n=1}^\infty(1+n^{-s})=\gamma$

Euler's "On transcendental progressions..." [E19]

Alternate proof for Viète's infinite product of nested radicals

Does $\prod_{k=1}^\infty 1- \frac{1}{k^\alpha}$ converge for $\alpha >1$?

Understanding the proof of $\text{Theorem (8.1.7)}$ in Greene's Function Theory of One Complex Varible?

Proving the convergence of $\bigg (\sum_{n}^{\nu} \bigg( \sum_{n}^{\chi} |\log(p_{n})+\log(q_{n})| \bigg ) \bigg )$?

Why do we have $ \ln(z) = \frac{z-1}{e -1} \prod_{n = 1}^{\infty} \frac{ \exp(2^{-n}) +1} {z^{2^{-n}} + 1} $

Derivatives of Infinite Product that Diverges to 0

Does $\prod \limits_{n=2}^{\infty }\left(1+\frac{1}{n\,\ln(n)}\right)$ converge?

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