Question

Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$

score 363 · Answer 1 · 2013-07-25 18:52:02

363

Views

Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$

Published on 25 Jul 2013 - 18:52

score 154 · Answer 2 · 2013-07-27 14:45:54

154

Views

Closed form for the product $G(x)G(-x)$ of two Barnes functions

Published on 27 Jul 2013 - 14:45

score 212 · Answer 3 · 2013-07-29 19:47:15

212

Views

$\sin(x)$ infinite product

Published on 29 Jul 2013 - 19:47

score 16.5k · Answer 4 · 2013-07-30 23:39:58

16.5k

Views

Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $

Published on 30 Jul 2013 - 23:39

score 2k · Answer 5 · 2013-07-31 06:12:25

2k

Views

Conversion of sum of series into product form: $\sum_{n=1}^\infty \frac1{n(n+1)} = \frac12 \prod_{n=2}^\infty \left( 1+\frac{1}{n^2-1} \right)$

Published on 31 Jul 2013 - 6:12

score 102 · Answer 6 · 2013-07-31 21:55:21

102

Views

How to write $r(a) = \lim_{n\to∞}r_n(a)$ as an infinite product?

Published on 31 Jul 2013 - 21:55

score 589 · Answer 7 · 2013-08-04 15:43:07

589

Views

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$

Published on 04 Aug 2013 - 15:43

score 298 · Answer 8 · 2013-08-04 20:37:11

298

Views

Infinite product of rotation matrices

Published on 04 Aug 2013 - 20:37

score 1.7k · Answer 9 · 2013-08-05 20:04:01

1.7k

Views

How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$?

Published on 05 Aug 2013 - 20:04

score 1k · Answer 10 · 2013-08-07 17:10:11

1k

Views

How to compute $\prod\limits^{\infty}_{n=2} \frac{n^3-1}{n^3+1}$

Published on 07 Aug 2013 - 17:10

score 1.7k · Answer 11 · 2013-08-09 16:21:37

1.7k

Views

What is the product of this by telescopic method?

Published on 09 Aug 2013 - 16:21

score 210 · Answer 12 · 2026-03-31 20:09:09

210

Views

Weierstrass product expression for Klein's j-invariant

Published on 31 Mar 2026 - 20:09

score 111 · Answer 13 · 2013-08-19 16:09:25

111

Views

Trying to figure out why for $n>1$ it's true that $\prod_{j=n}^{\infty} (1-2^{-j+1}) \geq 1/4$.

Published on 19 Aug 2013 - 16:09

score 143 · Answer 14 · 2026-03-26 03:12:34

143

Views

Assuming there exist infinite prime twins does $\prod_i (1+\frac{1}{p_i})$ diverge?

Published on 26 Mar 2026 - 3:12

score 3.3k · Answer 15 · 2013-09-12 20:03:26

3.3k

Views

What's the limit of $\prod_1^\infty \left(1-\frac{1}{2^n}\right)=(1-1/2)(1-1/4)(1-1/8)...$?

Published on 12 Sep 2013 - 20:03

List Question

Finding the limit of roots products $(\sqrt{2}-\sqrt[3]{2})(\sqrt{2}-\sqrt[4]{2})(\sqrt{2}-\sqrt[5]{2})\cdot \cdot \cdot (\sqrt{2}-\sqrt[n]{2})$

Closed form for the product $G(x)G(-x)$ of two Barnes functions

$\sin(x)$ infinite product

Finding the limit $\lim \limits_{n \to \infty}\ (\cos \frac x 2 \cdot\cos \frac x 4\cdot \cos \frac x 8\cdots \cos \frac x {2^n}) $

Conversion of sum of series into product form: $\sum_{n=1}^\infty \frac1{n(n+1)} = \frac12 \prod_{n=2}^\infty \left( 1+\frac{1}{n^2-1} \right)$

How to write $r(a) = \lim_{n\to∞}r_n(a)$ as an infinite product?

Find the value of $3^9\cdot 3^3\cdot 3\cdot 3^{1/3}\cdot\cdots$

Infinite product of rotation matrices

How to compute $\prod_{n=1}^\infty\left(1+\frac{1}{n!}\right)$?

How to compute $\prod\limits^{\infty}_{n=2} \frac{n^3-1}{n^3+1}$

What is the product of this by telescopic method?

Weierstrass product expression for Klein's j-invariant

Trying to figure out why for $n>1$ it's true that $\prod_{j=n}^{\infty} (1-2^{-j+1}) \geq 1/4$.

Assuming there exist infinite prime twins does $\prod_i (1+\frac{1}{p_i})$ diverge?

What's the limit of $\prod_1^\infty \left(1-\frac{1}{2^n}\right)=(1-1/2)(1-1/4)(1-1/8)...$?

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