Question

Infinite roots inside roots

score 89 · Answer 1 · 2023-10-01 05:54:21

89

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Infinite roots inside roots

Published on 01 Oct 2023 - 5:54

score 528 · Answer 2 · 2023-10-04 15:50:02

528

Views

$(1\pm\frac{1}{3})(1\pm\frac{1}{5})(1\pm\frac{1}{7})(1\pm\frac{1}{9})(1\pm\frac{1}{11})\cdots$ and related products

Published on 04 Oct 2023 - 15:50

score 35 · Answer 3 · 2023-10-07 16:36:45

35

Views

Every real $x\in [1,2]$ can be written as infinite product $\prod(1+b_k2^{-k})$ with $b_k \in\{0, 1\}$

Published on 07 Oct 2023 - 16:36

score 202 · Answer 4 · 2023-10-07 18:22:31

202

Views

Calculation of a non-trivial integral of exponential

Published on 07 Oct 2023 - 18:22

score 152 · Answer 5 · 2023-10-18 19:22:59

152

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Is there a closed form for $b_{n,m}(x)=\sum_{i=1}^m \frac{b_{n-1,i}(1)}{4i^2-1}x^i$?

Published on 18 Oct 2023 - 19:22

score 93 · Answer 6 · 2023-10-28 06:32:47

93

Views

Please verify this infinite product representation of $2+\sqrt{3}-\sqrt{2}-\sqrt{6}$

Published on 28 Oct 2023 - 6:32

score 72 · Answer 7 · 2023-11-06 04:57:57

72

Views

The quotient of the product of all positive odd numbers and the product of all natural numbers

Published on 06 Nov 2023 - 4:57

score 1k · Answer 8 · 2026-03-28 10:41:29

1k

Views

A curious coincidence: $\prod\limits_{k=1}^\infty\left(1+\int_{k}^{k+1}\left(\frac{\sin (\pi x)}{x}\right)^2\mathrm dx\right)\overset{?}{=}\pi/2$

Published on 28 Mar 2026 - 10:41

score 115 · Answer 9 · 2023-11-11 15:02:25

115

Views

Is there a sequence of unique terms $\{a_k\}$ such that $\sum\limits_{k=1}^\infty a_k=\prod\limits_{k=1}^\infty (1+a_k)\ne0$?

Published on 11 Nov 2023 - 15:02

score 48 · Answer 10 · 2023-11-11 22:52:54

48

Views

Does $\prod_{n=1}^\infty (1-\frac{z^2}{(2n\pi i)^2})=\frac{e^z-1}{z}$?

Published on 11 Nov 2023 - 22:52

score 225 · Answer 11 · 2023-11-13 08:57:44

225

Views

Why does $(1 + x)(1 + x^2)(1 + x^4)(1+x^8) \cdots = 1 + x + x^2 + x^3 + \cdots$?

Published on 13 Nov 2023 - 8:57

score 181 · Answer 12 · 2026-03-27 04:16:35

181

Views

Can we formally multiply out infinite products?

Published on 27 Mar 2026 - 4:16

score 28 · Answer 13 · 2023-11-14 10:30:31

28

Views

Problem on convergence of infinite product

Published on 14 Nov 2023 - 10:30

score 98 · Answer 14 · 2023-11-17 21:19:08

98

Views

confusion regarding infinite cartesian product

Published on 17 Nov 2023 - 21:19

score 192 · Answer 15 · 2026-03-27 06:17:01

192

Views

Find the value of $\frac{1}{2}^{\frac{1}{3}^{\frac{1}{4}^{\cdots \infty}}}$?

Published on 27 Mar 2026 - 6:17

List Question

Infinite roots inside roots

$(1\pm\frac{1}{3})(1\pm\frac{1}{5})(1\pm\frac{1}{7})(1\pm\frac{1}{9})(1\pm\frac{1}{11})\cdots$ and related products

Every real $x\in [1,2]$ can be written as infinite product $\prod(1+b_k2^{-k})$ with $b_k \in\{0, 1\}$

Calculation of a non-trivial integral of exponential

Is there a closed form for $b_{n,m}(x)=\sum_{i=1}^m \frac{b_{n-1,i}(1)}{4i^2-1}x^i$?

Please verify this infinite product representation of $2+\sqrt{3}-\sqrt{2}-\sqrt{6}$

The quotient of the product of all positive odd numbers and the product of all natural numbers

A curious coincidence: $\prod\limits_{k=1}^\infty\left(1+\int_{k}^{k+1}\left(\frac{\sin (\pi x)}{x}\right)^2\mathrm dx\right)\overset{?}{=}\pi/2$

Is there a sequence of unique terms $\{a_k\}$ such that $\sum\limits_{k=1}^\infty a_k=\prod\limits_{k=1}^\infty (1+a_k)\ne0$?

Does $\prod_{n=1}^\infty (1-\frac{z^2}{(2n\pi i)^2})=\frac{e^z-1}{z}$?

Why does $(1 + x)(1 + x^2)(1 + x^4)(1+x^8) \cdots = 1 + x + x^2 + x^3 + \cdots$?

Can we formally multiply out infinite products?

Problem on convergence of infinite product

confusion regarding infinite cartesian product

Find the value of $\frac{1}{2}^{\frac{1}{3}^{\frac{1}{4}^{\cdots \infty}}}$?

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