Question

Is this infinite product formula for Apéry's constant correct $\zeta(3)=\frac{\pi^3}{28}\prod_{n=1}^\infty \ln(1+1/n)(n+1/2)$?

score 285 · Answer 1 · 2019-07-08 21:35:01

285

Views

Is this infinite product formula for Apéry's constant correct $\zeta(3)=\frac{\pi^3}{28}\prod_{n=1}^\infty \ln(1+1/n)(n+1/2)$?

Published on 08 Jul 2019 - 21:35

score 54 · Answer 2 · 2019-07-09 02:44:23

54

Views

Infinite product in terms of a special function or integral

Published on 09 Jul 2019 - 2:44

score 57 · Answer 3 · 2019-07-12 09:11:35

57

Views

Are there good bounds for $\prod_{n=1}^m (1+a_n)$ when $\sum a_n$ diverges?

Published on 12 Jul 2019 - 9:11

score 187 · Answer 4 · 2019-07-18 06:24:53

187

Views

Eliminating remainder in formulation of Riemann zeta function formula

Published on 18 Jul 2019 - 6:24

score 109 · Answer 5 · 2019-07-20 06:48:55

109

Views

Did Euler Mistakenly Try to Extend a Property of a Finite Product to an Infinite One?

Published on 20 Jul 2019 - 6:48

score 203 · Answer 6 · 2026-03-26 06:32:40

203

Views

Conjecture: ${_2 F_1} \left(\frac{1}{2}- \frac{x}{2},1- \frac{x}{2};2;1 \right)=\prod_{n=2}^\infty \frac{(2n-2+x)(2n-1+x)}{2n (2n-3+2x)}$

Published on 26 Mar 2026 - 6:32

score 1.8k · Answer 7 · 2019-07-31 05:33:51

1.8k

Views

How to calculate infinite product of $(2^n-1)/2^n$??

Published on 31 Jul 2019 - 5:33

score 132 · Answer 8 · 2026-03-25 14:25:29

132

Views

Closed form for $\lim_{n \to \infty} \frac{n!}{\pi^n x^n} \prod_{k=1}^n \sin \frac{\pi x}{k}$

Published on 25 Mar 2026 - 14:25

score 58 · Answer 9 · 2019-08-06 09:55:57

58

Views

Infinite matrix product of matrix with an infinitesimal variable, and a constant quantity.

Published on 06 Aug 2019 - 9:55

score 48 · Answer 10 · 2019-08-07 09:46:51

48

Views

Fourier transform of a Weierstraß product

Published on 07 Aug 2019 - 9:46

score 221 · Answer 11 · 2026-03-25 09:47:13

221

Views

Curious closed forms of the $q$-Gamma function.

Published on 25 Mar 2026 - 9:47

score 138 · Answer 12 · 2026-03-26 08:02:35

138

Views

Evaluating the product containing the reciprocals of all primes $\prod_{k=1}^\infty\left(1+\frac{(-1)^k}{p_k}\right)$

Published on 26 Mar 2026 - 8:02

score 59 · Answer 13 · 2026-03-25 09:32:14

59

Views

In the group $\bigoplus_{j=-\infty}^{\infty} G$ does $a \cdot_k b = (a_{j+k} b_j)$ also form a group?

Published on 25 Mar 2026 - 9:32

score 76 · Answer 14 · 2019-08-21 19:01:26

76

Views

Infinite product proof without using gamma function

Published on 21 Aug 2019 - 19:01

score 129 · Answer 15 · 2026-03-25 09:49:57

129

Views

Coefficients of polynomial $f_n(q)=\prod_{k=1}^{n}(1+q^k)$

Published on 25 Mar 2026 - 9:49

List Question

Is this infinite product formula for Apéry's constant correct $\zeta(3)=\frac{\pi^3}{28}\prod_{n=1}^\infty \ln(1+1/n)(n+1/2)$?

Infinite product in terms of a special function or integral

Are there good bounds for $\prod_{n=1}^m (1+a_n)$ when $\sum a_n$ diverges?

Eliminating remainder in formulation of Riemann zeta function formula

Did Euler Mistakenly Try to Extend a Property of a Finite Product to an Infinite One?

Conjecture: ${_2 F_1} \left(\frac{1}{2}- \frac{x}{2},1- \frac{x}{2};2;1 \right)=\prod_{n=2}^\infty \frac{(2n-2+x)(2n-1+x)}{2n (2n-3+2x)}$

How to calculate infinite product of $(2^n-1)/2^n$??

Closed form for $\lim_{n \to \infty} \frac{n!}{\pi^n x^n} \prod_{k=1}^n \sin \frac{\pi x}{k}$

Infinite matrix product of matrix with an infinitesimal variable, and a constant quantity.

Fourier transform of a Weierstraß product

Curious closed forms of the $q$-Gamma function.

Evaluating the product containing the reciprocals of all primes $\prod_{k=1}^\infty\left(1+\frac{(-1)^k}{p_k}\right)$

In the group $\bigoplus_{j=-\infty}^{\infty} G$ does $a \cdot_k b = (a_{j+k} b_j)$ also form a group?

Infinite product proof without using gamma function

Coefficients of polynomial $f_n(q)=\prod_{k=1}^{n}(1+q^k)$

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