Question

Can $\prod_{n=1}^\infty(1+e^{2\pi i n\tau})$ be expressed in terms of the Euler Phi Function?

score 50 · Answer 1 · 2018-09-04 13:59:23

50

Views

Can $\prod_{n=1}^\infty(1+e^{2\pi i n\tau})$ be expressed in terms of the Euler Phi Function?

Published on 04 Sep 2018 - 13:59

score 202 · Answer 2 · 2018-09-07 09:35:55

202

Views

Finding the value of $\prod_{n=0}^\infty a_n$ with $a_0=1/2$ and $a_{n}=1+(a_{n-1}-1)^2$

Published on 07 Sep 2018 - 9:35

score 123 · Answer 3 · 2026-03-25 04:35:34

123

Views

How does this infinite product work?

Published on 25 Mar 2026 - 4:35

score 134 · Answer 4 · 2026-03-25 16:03:36

134

Views

let define the "waved" factorial as $\prod_{i=1}^n (\text{if } \bmod(i,2)=={0\text{ or } 1}\text{ then } [2/i] \text{ else } [i])$

Published on 25 Mar 2026 - 16:03

score 251 · Answer 5 · 2018-09-22 09:42:10

251

Views

What topology do we give the set of polynomial functions

Published on 22 Sep 2018 - 9:42

score 191 · Answer 6 · 2018-09-24 12:05:44

191

Views

Manipulating infinite products (Hadamard product for the Riemann Zeta)

Published on 24 Sep 2018 - 12:05

score 580 · Answer 7 · 2018-09-26 16:47:07

580

Views

How to prove the set of bounded sequences is clopen in the uniform metric?

Published on 26 Sep 2018 - 16:47

score 456 · Answer 8 · 2018-09-28 08:20:52

456

Views

For each $\beta \in(0,1)$, give a sequence $\{a_j\}\subset(0,1)$ with $\prod (1-\alpha_j) = \beta $

Published on 28 Sep 2018 - 8:20

score 69 · Answer 9 · 2026-03-25 11:01:41

69

Views

Closed form of this product or approximate?

Published on 25 Mar 2026 - 11:01

score 78 · Answer 10 · 2018-09-30 17:57:16

78

Views

Why is $\prod_{n=1}^\infty \dfrac{(1+1/n)^s}{1+s/n}$ convergent for $s$ complex with $Re(s)>0$?

Published on 30 Sep 2018 - 17:57

score 120 · Answer 11 · 2018-09-30 19:03:53

120

Views

On $\sin x=x \cdot \prod_{n=1}^{\infty}(1-(\frac{x}{\pi n})^2)$

Published on 30 Sep 2018 - 19:03

score 101 · Answer 12 · 2026-03-25 04:35:04

101

Views

Infinite sum $S(k) = \lambda + 2^k \lambda^2 + 3^k \lambda^3 + \dots$

Published on 25 Mar 2026 - 4:35

score 104 · Answer 13 · 2018-10-08 17:32:13

104

Views

Convergence of $P=\prod_{k=1}^{\infty}\left(1+\frac{1}{5^k}\right) $

Published on 08 Oct 2018 - 17:32

score 498 · Answer 14 · 2018-10-10 06:15:30

498

Views

Why is the proof of "countable many product of countable sets is countable" wrong?

Published on 10 Oct 2018 - 6:15

score 77 · Answer 15 · 2026-03-24 21:08:30

77

Views

Is the sequence of real number that are $0$ from some point Sense in the box or product topologies

Published on 24 Mar 2026 - 21:08

List Question

Can $\prod_{n=1}^\infty(1+e^{2\pi i n\tau})$ be expressed in terms of the Euler Phi Function?

Finding the value of $\prod_{n=0}^\infty a_n$ with $a_0=1/2$ and $a_{n}=1+(a_{n-1}-1)^2$

How does this infinite product work?

let define the "waved" factorial as $\prod_{i=1}^n (\text{if } \bmod(i,2)=={0\text{ or } 1}\text{ then } [2/i] \text{ else } [i])$

What topology do we give the set of polynomial functions

Manipulating infinite products (Hadamard product for the Riemann Zeta)

How to prove the set of bounded sequences is clopen in the uniform metric?

For each $\beta \in(0,1)$, give a sequence $\{a_j\}\subset(0,1)$ with $\prod (1-\alpha_j) = \beta $

Closed form of this product or approximate?

Why is $\prod_{n=1}^\infty \dfrac{(1+1/n)^s}{1+s/n}$ convergent for $s$ complex with $Re(s)>0$?

On $\sin x=x \cdot \prod_{n=1}^{\infty}(1-(\frac{x}{\pi n})^2)$

Infinite sum $S(k) = \lambda + 2^k \lambda^2 + 3^k \lambda^3 + \dots$

Convergence of $P=\prod_{k=1}^{\infty}\left(1+\frac{1}{5^k}\right) $

Why is the proof of "countable many product of countable sets is countable" wrong?

Is the sequence of real number that are $0$ from some point Sense in the box or product topologies

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