Question

Can $\prod_{n=0}^{\infty}\left(1+ \frac{1}{2^n}\right)$ be expressed in terms of the Pell constant?

score 101 · Answer 1 · 2026-03-25 21:31:32

101

Views

Can $\prod_{n=0}^{\infty}\left(1+ \frac{1}{2^n}\right)$ be expressed in terms of the Pell constant?

Published on 25 Mar 2026 - 21:31

score 48 · Answer 2 · 2020-06-12 19:12:12

48

Views

The form of an infinite product that converges to 1/2 or 1/3

Published on 12 Jun 2020 - 19:12

score 64 · Answer 3 · 2020-06-12 19:30:01

64

Views

$\prod_{i=1}^\infty\left(\frac{i+x}{i+1}\right)^{1/i}\stackrel{?}{=}x$

Published on 12 Jun 2020 - 19:30

score 487 · Answer 4 · 2026-03-25 20:33:53

487

Views

A formula for Ramanujan's tau function

Published on 25 Mar 2026 - 20:33

score 95 · Answer 5 · 2020-06-15 16:19:21

95

Views

Can we find a closed form for $\sum _{i=0}^{\infty } ((-1)^{i}x^i\prod_{j=1}^{i}\frac{e^j}{e^j-1})$?

Published on 15 Jun 2020 - 16:19

score 71 · Answer 6 · 2020-06-16 21:46:36

71

Views

Derivative of ln of infinite product.

Published on 16 Jun 2020 - 21:46

score 379 · Answer 7 · 2020-06-24 07:29:05

379

Views

Is there any closed form for $\displaystyle \prod_{n=1}^{\infty} \left(1-\frac{1}{\zeta(n)}\right)$

Published on 24 Jun 2020 - 7:29

score 80 · Answer 8 · 2020-06-24 22:33:38

80

Views

Are there any values of $m$ other than $3$ such that $\prod_{k=2}^{\infty}\dfrac{(k^m-1)}{ (k^m+1)} $ has some kind of known form?

Published on 24 Jun 2020 - 22:33

score 639 · Answer 9 · 2026-03-25 10:21:49

639

Views

If $\sum a_n^k$ converges for all $k \geq 1$, does $\prod (1 + a_n)$ converge?

Published on 25 Mar 2026 - 10:21

score 116 · Answer 10 · 2020-06-30 22:19:55

If $\sum_{n=1}^{\infty} a_n$ converges and $\sum_{n=1}^{\infty} a_n^2$ diverges, then $\prod_{n=1}^{\infty} (1+a_n)$ diverges to $0$.

score 49 · Answer 11 · 2020-07-01 02:44:54

49

Views

Help with straight-forward proof of product involving Gamma functions

Published on 01 Jul 2020 - 2:44

score 76 · Answer 12 · 2026-03-26 21:27:30

76

Views

Infinite product of transcendental numbers approaches 1

Published on 26 Mar 2026 - 21:27

score 180 · Answer 13 · 2020-07-03 14:24:23

180

Views

Evaluating the $ \lim_{n \to \infty} \prod_{1\leq k \leq n} (1+\frac{k}{n})^{1/k}$

Published on 03 Jul 2020 - 14:24

score 171 · Answer 14 · 2026-03-25 23:40:28

171

Views

Riemann hypothesis equivalent to $\prod \left(\frac{4 w_i^2 + 9}{4 w_i^2 + 1}\right) = \prod (1 - 2/v_i) = \frac{\pi}{6}$ ??

Published on 25 Mar 2026 - 23:40

score 310 · Answer 15 · 2026-03-25 11:54:09

310

Views

Convergence of Euler product implies convergence of Dirichlet series?

Published on 25 Mar 2026 - 11:54

List Question

Can $\prod_{n=0}^{\infty}\left(1+ \frac{1}{2^n}\right)$ be expressed in terms of the Pell constant?

The form of an infinite product that converges to 1/2 or 1/3

$\prod_{i=1}^\infty\left(\frac{i+x}{i+1}\right)^{1/i}\stackrel{?}{=}x$

A formula for Ramanujan's tau function

Can we find a closed form for $\sum _{i=0}^{\infty } ((-1)^{i}x^i\prod_{j=1}^{i}\frac{e^j}{e^j-1})$?

Derivative of ln of infinite product.

Is there any closed form for $\displaystyle \prod_{n=1}^{\infty} \left(1-\frac{1}{\zeta(n)}\right)$

Are there any values of $m$ other than $3$ such that $\prod_{k=2}^{\infty}\dfrac{(k^m-1)}{ (k^m+1)} $ has some kind of known form?

If $\sum a_n^k$ converges for all $k \geq 1$, does $\prod (1 + a_n)$ converge?

If $\sum_{n=1}^{\infty} a_n$ converges and $\sum_{n=1}^{\infty} a_n^2$ diverges, then $\prod_{n=1}^{\infty} (1+a_n)$ diverges to $0$.

Help with straight-forward proof of product involving Gamma functions

Infinite product of transcendental numbers approaches 1

Evaluating the $ \lim_{n \to \infty} \prod_{1\leq k \leq n} (1+\frac{k}{n})^{1/k}$

Riemann hypothesis equivalent to $\prod \left(\frac{4 w_i^2 + 9}{4 w_i^2 + 1}\right) = \prod (1 - 2/v_i) = \frac{\pi}{6}$ ??

Convergence of Euler product implies convergence of Dirichlet series?

Trending Questions

Popular # Hahtags

Popular Questions