Question

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

score 53 · Answer 1 · 2026-04-15 00:37:13

53

Views

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

Published on 15 Apr 2026 - 0:37

score 205 · Answer 2 · 2026-04-16 19:13:28

205

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 16 Apr 2026 - 19:13

score 127 · Answer 3 · 2026-05-10 16:30:31

127

Views

How does this infinite product work?

Published on 10 May 2026 - 16:30

score 136 · Answer 4 · 2026-04-17 13:00:30

136

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 17 Apr 2026 - 13:00

score 254 · Answer 5 · 2026-04-14 03:12:48

254

Views

What topology do we give the set of polynomial functions

Published on 14 Apr 2026 - 3:12

score 194 · Answer 6 · 2026-04-15 05:00:02

194

Views

Manipulating infinite products (Hadamard product for the Riemann Zeta)

Published on 15 Apr 2026 - 5:00

score 582 · Answer 7 · 2026-04-15 12:56:48

582

Views

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

Published on 15 Apr 2026 - 12:56

score 459 · Answer 8 · 2026-04-17 03:00:36

459

Views

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

Published on 17 Apr 2026 - 3:00

score 72 · Answer 9 · 2026-05-10 22:07:42

72

Views

Closed form of this product or approximate?

Published on 10 May 2026 - 22:07

score 81 · Answer 10 · 2026-04-16 20:19:24

81

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 16 Apr 2026 - 20:19

score 123 · Answer 11 · 2026-04-16 18:43:13

123

Views

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

Published on 16 Apr 2026 - 18:43

score 104 · Answer 12 · 2026-05-10 13:44:53

104

Views

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

Published on 10 May 2026 - 13:44

score 106 · Answer 13 · 2026-04-15 06:40:25

106

Views

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

Published on 15 Apr 2026 - 6:40

score 501 · Answer 14 · 2026-04-14 05:51:53

501

Views

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

Published on 14 Apr 2026 - 5:51

score 86 · Answer 15 · 2026-05-10 15:30:24

86

Views

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

Published on 10 May 2026 - 15:30

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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