Question

Sequence without average density

score 39 · Answer 1 · 2020-07-17 06:39:04

39

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Sequence without average density

Published on 17 Jul 2020 - 6:39

score 147 · Answer 2 · 2020-07-17 10:43:39

147

Views

Does the category of $O_X$-Modules have exact products

Published on 17 Jul 2020 - 10:43

score 142 · Answer 3 · 2020-07-23 08:57:52

Prove $\prod_{n\ge0}^{ }\frac{\left(n+a\right)\left(n+b\right)}{\left(n+c\right)\left(n+d\right)}=\frac{\Gamma(c)\Gamma(d) }{ \Gamma(a)\Gamma(b)}$

score 173 · Answer 4 · 2020-07-23 09:13:59

173

Views

Closed-form expression for $\prod_{n=0}^{\infty}\frac{(4n+3)^{1/(4n+3)}}{(4n+5)^{1/(4n+5)}}$?

Published on 23 Jul 2020 - 9:13

score 100 · Answer 5 · 2026-03-26 11:00:45

100

Views

Convergence and absolute convergence of an infinite product of terms in $(0,1]$.

Published on 26 Mar 2026 - 11:00

score 48 · Answer 6 · 2020-07-24 16:16:02

48

Views

Prove if infinite product of $f(x)$ is $0$ then so is infinite product of $f(x\varphi)$

Published on 24 Jul 2020 - 16:16

score 42 · Answer 7 · 2020-07-26 15:23:09

42

Views

link between infinite sum and infinite product

Published on 26 Jul 2020 - 15:23

score 557 · Answer 8 · 2020-07-27 18:04:12

557

Views

Prove that the circumference of an ellipse is given by this infinite series

Published on 27 Jul 2020 - 18:04

score 423 · Answer 9 · 2020-07-30 03:32:47

423

Views

How to prove Stirling's formula. Using Wallis formula

Published on 30 Jul 2020 - 3:32

score 117 · Answer 10 · 2016-07-06 11:06:16

$\prod\limits_{k=0 \atop 2k+1\ne 0 \bmod n}^\infty \frac{2k+1+(-1)^{\lfloor (2k+1)/n\rfloor}}{2k+1}=\sqrt{n}$ for $n\ge 2$

score 223 · Answer 11 · 2026-03-25 23:39:22

223

Views

On calculations for $\prod_{k=2}^\infty \left( 1+\frac{\mu(k)}{k^3} x\right)$, where $\mu(n)$ is the Möbius function

Published on 25 Mar 2026 - 23:39

score 4.8k · Answer 12 · 2016-07-13 16:37:47

4.8k

Views

Does multiplying all a number's roots together give a product of infinity?

Published on 13 Jul 2016 - 16:37

score 623 · Answer 13 · 2016-07-13 20:01:26

623

Views

Two randomly chosen coprime integers

Published on 13 Jul 2016 - 20:01

score 297 · Answer 14 · 2016-07-13 21:30:02

297

Views

How do we prove that $4(3\sqrt2-4)=\prod_{n=1}^{\infty}\left({e^{2\pi(2n-1)}-1\over e^{2\pi(2n-1)}+1}\right)^8?$

Published on 13 Jul 2016 - 21:30

score 459 · Answer 15 · 2016-07-27 20:30:51

459

Views

Evaluate an infinite product in a closed form $\prod\limits_{n=1}^{\infty} \frac{1}{1+\pi^{1/{2^n}}}$

Published on 27 Jul 2016 - 20:30

List Question

Sequence without average density

Does the category of $O_X$-Modules have exact products

Prove $\prod_{n\ge0}^{ }\frac{\left(n+a\right)\left(n+b\right)}{\left(n+c\right)\left(n+d\right)}=\frac{\Gamma(c)\Gamma(d) }{ \Gamma(a)\Gamma(b)}$

Closed-form expression for $\prod_{n=0}^{\infty}\frac{(4n+3)^{1/(4n+3)}}{(4n+5)^{1/(4n+5)}}$?

Convergence and absolute convergence of an infinite product of terms in $(0,1]$.

Prove if infinite product of $f(x)$ is $0$ then so is infinite product of $f(x\varphi)$

link between infinite sum and infinite product

Prove that the circumference of an ellipse is given by this infinite series

How to prove Stirling's formula. Using Wallis formula

$\prod\limits_{k=0 \atop 2k+1\ne 0 \bmod n}^\infty \frac{2k+1+(-1)^{\lfloor (2k+1)/n\rfloor}}{2k+1}=\sqrt{n}$ for $n\ge 2$

On calculations for $\prod_{k=2}^\infty \left( 1+\frac{\mu(k)}{k^3} x\right)$, where $\mu(n)$ is the Möbius function

Does multiplying all a number's roots together give a product of infinity?

Two randomly chosen coprime integers

How do we prove that $4(3\sqrt2-4)=\prod_{n=1}^{\infty}\left({e^{2\pi(2n-1)}-1\over e^{2\pi(2n-1)}+1}\right)^8?$

Evaluate an infinite product in a closed form $\prod\limits_{n=1}^{\infty} \frac{1}{1+\pi^{1/{2^n}}}$

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