Question

Splitting infinite products up in a even and a odd part

score 857 · Answer 1 · 2018-08-01 14:57:23

857

Views

Splitting infinite products up in a even and a odd part

Published on 01 Aug 2018 - 14:57

score 66 · Answer 2 · 2018-08-01 17:05:03

66

Views

Prove $\prod_{k=2}^N\left(1-\frac{2}{k^3+1}\right)~=~\frac23\left(1+\frac1{N(N+1)}\right)$

Published on 01 Aug 2018 - 17:05

score 285 · Answer 3 · 2018-08-04 21:27:51

285

Views

Show that $\lim_{m \to \infty} \frac{2^{2m}m!(m+1)!}{(2m+1)!(2m+1)}=0$

Published on 04 Aug 2018 - 21:27

score 38 · Answer 4 · 2018-08-06 23:11:42

38

Views

Value of a specific q-series / infinite product?

Published on 06 Aug 2018 - 23:11

score 1.2k · Answer 5 · 2018-08-09 14:22:19

1.2k

Views

Evaluate the Sum $S=\frac{1}{4}+\frac{1.3}{4.6}+\frac{1.3.5}{4.6.8}+\cdots \infty$

Published on 09 Aug 2018 - 14:22

score 127 · Answer 6 · 2018-08-10 11:47:53

127

Views

Showing that $\lim_{n \rightarrow \infty} \prod_{k=m} (z + N_{k}) \rightarrow h(z)$ uniformly on compact subsets of $\mathbb{C}$?

Published on 10 Aug 2018 - 11:47

score 76 · Answer 7 · 2018-08-11 13:55:14

76

Views

A bound for the products of a bounded sequence $\{x_{k}\}$ with $\lim_{t\to \infty}\prod_{k=0}^{t}(1-x_{k})=0$

Published on 11 Aug 2018 - 13:55

score 34 · Answer 8 · 2018-08-11 16:11:54

34

Views

A guess on the bound of the product of bounded sequence $\{x_{k}\}$ with $\lim_{t\to\infty}\prod_{k=0}^{t}(1-x_{k})=0$ exponentially.

Published on 11 Aug 2018 - 16:11

score 721 · Answer 9 · 2018-08-12 09:48:46

721

Views

Infinite product $\prod\limits_{n=1}^\infty\cos( 1/n)$

Published on 12 Aug 2018 - 9:48

score 98 · Answer 10 · 2026-03-24 23:42:48

98

Views

Relation between infinite product and regularized product

Published on 24 Mar 2026 - 23:42

score 73 · Answer 11 · 2018-08-13 19:51:15

73

Views

Alternate ways of showing that $\lim_{n \rightarrow \infty} \sum_{n}^{\infty}g_{n}(z_{n}) = \sum_{k}^{\infty} g_{n}(z) $?

Published on 13 Aug 2018 - 19:51

score 251 · Answer 12 · 2018-08-14 18:06:23

251

Views

Evaluate $\sum_{n=0}^\infty (-1)^n \ln\frac{2+2n}{1+2n}$

Published on 14 Aug 2018 - 18:06

score 363 · Answer 13 · 2026-03-25 04:41:46

363

Views

Proving that the sequence $1, \frac12, \frac{1/2}{3/4}, \cdots$ converges to $\frac{\sqrt 2}2$

Published on 25 Mar 2026 - 4:41

score 408 · Answer 14 · 2018-08-27 11:04:28

408

Views

Factorization $\cos\left(\tfrac{\pi z}{4}\right)-\sin\left(\tfrac{\pi z}{4}\right)$

Published on 27 Aug 2018 - 11:04

score 93 · Answer 15 · 2026-03-25 17:42:28

93

Views

Evaluating $\sum\limits_{n \ge 0} \frac{1}{x^{2^n}-y^{2^n}}$ where $x, y \in \mathbb R^{+}$ and $x \ne y, x>1.$

Published on 25 Mar 2026 - 17:42

List Question

Splitting infinite products up in a even and a odd part

Prove $\prod_{k=2}^N\left(1-\frac{2}{k^3+1}\right)~=~\frac23\left(1+\frac1{N(N+1)}\right)$

Show that $\lim_{m \to \infty} \frac{2^{2m}m!(m+1)!}{(2m+1)!(2m+1)}=0$

Value of a specific q-series / infinite product?

Evaluate the Sum $S=\frac{1}{4}+\frac{1.3}{4.6}+\frac{1.3.5}{4.6.8}+\cdots \infty$

Showing that $\lim_{n \rightarrow \infty} \prod_{k=m} (z + N_{k}) \rightarrow h(z)$ uniformly on compact subsets of $\mathbb{C}$?

A bound for the products of a bounded sequence $\{x_{k}\}$ with $\lim_{t\to \infty}\prod_{k=0}^{t}(1-x_{k})=0$

A guess on the bound of the product of bounded sequence $\{x_{k}\}$ with $\lim_{t\to\infty}\prod_{k=0}^{t}(1-x_{k})=0$ exponentially.

Infinite product $\prod\limits_{n=1}^\infty\cos( 1/n)$

Relation between infinite product and regularized product

Alternate ways of showing that $\lim_{n \rightarrow \infty} \sum_{n}^{\infty}g_{n}(z_{n}) = \sum_{k}^{\infty} g_{n}(z) $?

Evaluate $\sum_{n=0}^\infty (-1)^n \ln\frac{2+2n}{1+2n}$

Proving that the sequence $1, \frac12, \frac{1/2}{3/4}, \cdots$ converges to $\frac{\sqrt 2}2$

Factorization $\cos\left(\tfrac{\pi z}{4}\right)-\sin\left(\tfrac{\pi z}{4}\right)$

Evaluating $\sum\limits_{n \ge 0} \frac{1}{x^{2^n}-y^{2^n}}$ where $x, y \in \mathbb R^{+}$ and $x \ne y, x>1.$

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