Question

If $\alpha$ is the nth root of unity , then the value of

score 205 · Answer 1 · 2022-04-30 05:38:51

205

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If $\alpha$ is the nth root of unity , then the value of

Published on 30 Apr 2022 - 5:38

score 131 · Answer 2 · 2022-05-08 13:13:11

131

Views

For what infinite series can a closed form be obtained by means of the $\text{Sum} = \text{Product} $ method?

Published on 08 May 2022 - 13:13

score 55 · Answer 3 · 2022-05-16 15:10:19

55

Views

Proving that this infinite product is convergent

Published on 16 May 2022 - 15:10

score 230 · Answer 4 · 2026-03-25 11:09:36

230

Views

Factorization of modular forms using zeros and poles

Published on 25 Mar 2026 - 11:09

score 42 · Answer 5 · 2022-05-25 01:44:05

42

Views

Infinite product converging arbitrarily slowly to limit

Published on 25 May 2022 - 1:44

score 75 · Answer 6 · 2022-05-25 13:42:35

75

Views

How to compute $\displaystyle\prod_{i = 1}^{\infty} \frac{x^{i}}{e^{i!}}$?

Published on 25 May 2022 - 13:42

score 70 · Answer 7 · 2022-06-02 09:48:20

70

Views

Does there exist an example of converging infinite product when all elements are below 1?

Published on 02 Jun 2022 - 9:48

score 22 · Answer 8 · 2022-06-11 01:34:28

22

Views

Infinite Product of (1-x)^ib, as x approaches 1

Published on 11 Jun 2022 - 1:34

score 76 · Answer 9 · 2022-06-13 07:31:09

76

Views

Limit of $a_{n+1}=a_{n}\cdot \left( 1+\frac{1}{n}\right)$

Published on 13 Jun 2022 - 7:31

score 413 · Answer 10 · 2022-06-14 15:31:28

413

Views

Closed form for $\lim\limits_{n\to\infty}\prod\limits_{k=1}^n{\left(2-\frac{2n^2-\pi^2+8}{n^2}\cos{\frac{(2k-1)\pi}{n}}\right)}$?

Published on 14 Jun 2022 - 15:31

score 99 · Answer 11 · 2026-03-27 17:52:58

99

Views

$\lim_{n\to\infty}{(\text{median of}\prod_{i=1}^n{X_i})}$ where $X_i$ are independent uniform random real numbers from $0$ to $e$

Published on 27 Mar 2026 - 17:52

score 77 · Answer 12 · 2022-06-21 01:30:36

77

Views

Proving $ e^2 = e$?

Published on 21 Jun 2022 - 1:30

score 139 · Answer 13 · 2026-02-23 21:19:11

139

Views

There's this infinite geometric mean, or the infinity'th term of a sequence of finite means. I know what it converges to, but how do I prove it?

Published on 23 Feb 2026 - 21:19

score 103 · Answer 14 · 2026-03-25 11:16:35

103

Views

How to derive Weierstrass factorization for $\cos(z)$ from $\tan(z)=\sum_{n=0}^\infty \frac{8z}{(2n+1)^2\pi^2-4z^2}$

Published on 25 Mar 2026 - 11:16

score 63 · Answer 15 · 2022-06-28 01:41:29

63

Views

Is $\prod\limits_{n=1}^{\infty}\frac{p_{n}^{2}+1}{p_{n}^{2}-1} = 2.5$?

Published on 28 Jun 2022 - 1:41

List Question

If $\alpha$ is the nth root of unity , then the value of

For what infinite series can a closed form be obtained by means of the $\text{Sum} = \text{Product} $ method?

Proving that this infinite product is convergent

Factorization of modular forms using zeros and poles

Infinite product converging arbitrarily slowly to limit

How to compute $\displaystyle\prod_{i = 1}^{\infty} \frac{x^{i}}{e^{i!}}$?

Does there exist an example of converging infinite product when all elements are below 1?

Infinite Product of (1-x)^ib, as x approaches 1

Limit of $a_{n+1}=a_{n}\cdot \left( 1+\frac{1}{n}\right)$

Closed form for $\lim\limits_{n\to\infty}\prod\limits_{k=1}^n{\left(2-\frac{2n^2-\pi^2+8}{n^2}\cos{\frac{(2k-1)\pi}{n}}\right)}$?

$\lim_{n\to\infty}{(\text{median of}\prod_{i=1}^n{X_i})}$ where $X_i$ are independent uniform random real numbers from $0$ to $e$

Proving $ e^2 = e$?

There's this infinite geometric mean, or the infinity'th term of a sequence of finite means. I know what it converges to, but how do I prove it?

How to derive Weierstrass factorization for $\cos(z)$ from $\tan(z)=\sum_{n=0}^\infty \frac{8z}{(2n+1)^2\pi^2-4z^2}$

Is $\prod\limits_{n=1}^{\infty}\frac{p_{n}^{2}+1}{p_{n}^{2}-1} = 2.5$?

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