Question

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

score 83 · Answer 1 · 2026-04-29 12:49:13

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

score 164 · Answer 2 · 2026-04-29 12:49:08

164

Views

Infinite product of the form $2-2^{1/k}$

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score 830 · Answer 3 · 2026-04-29 12:49:12

830

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score 94 · Answer 4 · 2026-04-29 12:49:00

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Infinite product $\prod \frac{R^{2^n}+z^{z^n}}{R^{2^n}}$ coverges

Published on 29 Apr 2026 - 12:49

score 73 · Answer 5 · 2026-04-16 23:15:11

73

Views

Proof $1 \geq \prod_{k=m}^n\left\{ 1-\frac{\sin^2 \frac{x}{2n-1}}{\sin^2 \frac{k\pi}{2n-1}} \right\}$

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score 114 · Answer 6 · 2026-04-29 12:49:02

114

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score 233 · Answer 8 · 2026-04-29 12:49:06

233

Views

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score 319 · Answer 9 · 2026-04-29 12:49:01

319

Views

A very challenging question integral of an infinite product.

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score 330 · Answer 10 · 2026-04-29 12:48:52

330

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Example for infinite product topology

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score 321 · Answer 11 · 2026-04-29 12:49:11

321

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Question on infinite product of zeta function

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score 411 · Answer 12 · 2026-04-29 12:49:10

411

Views

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

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score 349 · Answer 13 · 2026-04-29 12:49:07

349

Views

Is there a rigorous way to define uncountable products?

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score 372 · Answer 14 · 2026-04-14 12:12:13

372

Views

Prove that ${\prod_\limits{n = k_0}^{\infty} (1 - a_n)} \;$ converges to positive value

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score 59 · Answer 15 · 2026-04-29 12:49:10

59

Views

Convergence of $\prod_{i=1}^{\infty}\cos(a^{-i}x)$

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List Question

$(3x- 3)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{2^{-n}}+1}=(x^3-1)\prod_{n = 1}^∞\frac{\exp(2^{-n})+1}{x^{3 \cdot 2^{-n}}+1}$

Infinite product of the form $2-2^{1/k}$

Continuous tensor products and integrals of such

Infinite product $\prod \frac{R^{2^n}+z^{z^n}}{R^{2^n}}$ coverges

Proof $1 \geq \prod_{k=m}^n\left\{ 1-\frac{\sin^2 \frac{x}{2n-1}}{\sin^2 \frac{k\pi}{2n-1}} \right\}$

Iteration of mapping with nested iterates in logarithm

If $Y=\left\{(x_i)\in\prod_i X_i| \{i\in I:x_i≠ p_i\} \text{ is finite}\right\}$ and $Y_F=\{(x_i)\in\prod_i X_i| i∉ F:x_i=p_i\}$ then $\bigcup Y_F=Y$

Are there any other ways for infinite product to diverge/converge to zero (other than two mentioned in description)

A very challenging question integral of an infinite product.

Example for infinite product topology

Question on infinite product of zeta function

A sequence $\{x_n\}$ is convergent in $\prod X_\alpha$ iff the projection sequence $\{\pi_\alpha(x_n)\}$ converges in $X_\alpha$ for any $\alpha$

Is there a rigorous way to define uncountable products?

Prove that ${\prod_\limits{n = k_0}^{\infty} (1 - a_n)} \;$ converges to positive value

Convergence of $\prod_{i=1}^{\infty}\cos(a^{-i}x)$

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