Question

Why $\frac{\sin(x)}{x} = (1-\frac{x^2}{\pi^2})(1-\frac{x^2}{4\pi^2})...$

score 93 · Answer 1 · 2020-05-09 04:55:38

93

Views

Why $\frac{\sin(x)}{x} = (1-\frac{x^2}{\pi^2})(1-\frac{x^2}{4\pi^2})...$

Published on 09 May 2020 - 4:55

score 135 · Answer 2 · 2026-03-28 06:06:48

135

Views

Metric in which consecutive primes have equivalent gaps?

Published on 28 Mar 2026 - 6:06

score 152 · Answer 3 · 2020-05-15 16:35:10

152

Views

Does $\prod_{m=1}^\infty \frac{1}{m^2}$ have a closed form?

Published on 15 May 2020 - 16:35

score 52 · Answer 4 · 2020-05-17 07:25:39

52

Views

If $S_n=\sum _{i=1}^n\frac{1}{a_i}$ and $a_k=\left(\prod _{i=1}^{k-1}a_i\right)+1$ then evaluate $\lim _{n\to \infty }S_n$.

Published on 17 May 2020 - 7:25

score 106 · Answer 5 · 2020-05-20 09:58:48

106

Views

Convergence of the product $\prod_{n=1}^{\infty}\left(1+\frac{x^n}{n^p}\right)\cos\frac{x^n}{n^q}$

Published on 20 May 2020 - 9:58

score 1.2k · Answer 6 · 2020-05-23 14:07:10

1.2k

Views

Evaluate $\lim_{n\to\infty} \prod_{k=1}^n \frac{2k}{2k-1}\int_{-1}^{\infty} \frac{{\left(\cos{x}\right)}^{2n}}{2^x} \; dx$

Published on 23 May 2020 - 14:07

score 183 · Answer 7 · 2026-03-28 15:21:21

183

Views

Product $\left[\sin(x)\cos\left(\frac{x}2\right)\right]^{1/2}\cdot\left[\sin\left(\frac{x}{2}\right) \cos \left(\frac{x}4\right)\right]^{1/4}\ \cdots$

Published on 28 Mar 2026 - 15:21

score 346 · Answer 8 · 2020-05-25 08:49:42

346

Views

infinite-dimensional inner product space

Published on 25 May 2020 - 8:49

score 187 · Answer 9 · 2020-05-26 11:41:10

187

Views

Sum $\sum \frac{1}{(4k-3)(4k-2)(4k-1)(4k)}$

Published on 26 May 2020 - 11:41

score 142 · Answer 10 · 2020-05-26 16:23:20

142

Views

Product representation of the exponential series.

Published on 26 May 2020 - 16:23

score 80 · Answer 11 · 2026-03-26 08:14:25

80

Views

A curious infinite product

Published on 26 Mar 2026 - 8:14

score 110 · Answer 12 · 2026-03-25 07:47:19

110

Views

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

Published on 25 Mar 2026 - 7:47

score 87 · Answer 13 · 2020-06-08 20:14:50

87

Views

Proof for any value of x greater than 1, the following statement is true: The limit of $\sum_{n=0}^{\infty} {\frac{1}{x ^ n}}$ is ${\frac{x}{x-1}}$

Published on 08 Jun 2020 - 20:14

score 332 · Answer 14 · 2020-06-09 17:11:05

332

Views

Infinite product integral $\int_{-\infty}^\infty \prod_{k=1}^\infty \cos\frac{x}{2^k}dx$

Published on 09 Jun 2020 - 17:11

score 153 · Answer 15 · 2026-03-26 11:01:21

153

Views

the convergence of the infinite product of matrices composed by matrces with the spectral radius less than 1

Published on 26 Mar 2026 - 11:01

List Question

Why $\frac{\sin(x)}{x} = (1-\frac{x^2}{\pi^2})(1-\frac{x^2}{4\pi^2})...$

Metric in which consecutive primes have equivalent gaps?

Does $\prod_{m=1}^\infty \frac{1}{m^2}$ have a closed form?

If $S_n=\sum _{i=1}^n\frac{1}{a_i}$ and $a_k=\left(\prod _{i=1}^{k-1}a_i\right)+1$ then evaluate $\lim _{n\to \infty }S_n$.

Convergence of the product $\prod_{n=1}^{\infty}\left(1+\frac{x^n}{n^p}\right)\cos\frac{x^n}{n^q}$

Evaluate $\lim_{n\to\infty} \prod_{k=1}^n \frac{2k}{2k-1}\int_{-1}^{\infty} \frac{{\left(\cos{x}\right)}^{2n}}{2^x} \; dx$

Product $\left[\sin(x)\cos\left(\frac{x}2\right)\right]^{1/2}\cdot\left[\sin\left(\frac{x}{2}\right) \cos \left(\frac{x}4\right)\right]^{1/4}\ \cdots$

infinite-dimensional inner product space

Sum $\sum \frac{1}{(4k-3)(4k-2)(4k-1)(4k)}$

Product representation of the exponential series.

A curious infinite product

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

Proof for any value of x greater than 1, the following statement is true: The limit of $\sum_{n=0}^{\infty} {\frac{1}{x ^ n}}$ is ${\frac{x}{x-1}}$

Infinite product integral $\int_{-\infty}^\infty \prod_{k=1}^\infty \cos\frac{x}{2^k}dx$

the convergence of the infinite product of matrices composed by matrces with the spectral radius less than 1

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