Question

Finding the closed form of $\prod _{n=0}^{\infty }\left(1\:-\:x^{2^n}+x^{2^{n+1}}\right)$

score 79 · Answer 1 · 2021-04-05 18:52:08

79

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Finding the closed form of $\prod _{n=0}^{\infty }\left(1\:-\:x^{2^n}+x^{2^{n+1}}\right)$

Published on 05 Apr 2021 - 18:52

score 53 · Answer 2 · 2026-04-01 14:44:28

53

Views

Convergent Infinite Product in Proof of Partitions Identity

Published on 01 Apr 2026 - 14:44

score 1k · Answer 3 · 2026-03-25 16:09:12

1k

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Proving that odd partitions and distinct partitions are equal

Published on 25 Mar 2026 - 16:09

score 226 · Answer 4 · 2021-04-07 12:57:46

226

Views

Closed form of the sum $\sum _{n=1}^{\infty }\:\left(\frac{1}{x^2-n^2\pi ^2}\right)$

Published on 07 Apr 2021 - 12:57

score 306 · Answer 5 · 2021-04-07 19:45:44

306

Views

Approximate result for $\prod_{n=1}^\infty\left(1-\frac{1}{2^n}\right)$?

Published on 07 Apr 2021 - 19:45

score 86 · Answer 6 · 2021-04-08 20:31:04

86

Views

Convergence of series $\sum \arcsin\left(\frac{r_n \sin(\theta_n)}{\sqrt{1+2r_n\cos(\theta_n)+r_n^2}}\right)$

Published on 08 Apr 2021 - 20:31

score 216 · Answer 7 · 2026-02-23 19:23:24

216

Views

e to an integral as an infinite product via the definition of the integral

Published on 23 Feb 2026 - 19:23

score 239 · Answer 8 · 2026-03-30 11:59:25

239

Views

Showing $\sinh z=z\prod_{n=1}^\infty\left(1+\frac{z^2}{n^2\pi^2}\right)$, given $\sin z=z\prod_{n=1}^{ \infty}\left(1 - \frac{z^2}{n^2\pi^2}\right)$

Published on 30 Mar 2026 - 11:59

score 52 · Answer 9 · 2026-03-25 09:29:57

52

Views

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Published on 25 Mar 2026 - 9:29

score 78 · Answer 10 · 2021-04-26 02:14:51

78

Views

Solutions of $((a-1)!)^x=0$

Published on 26 Apr 2021 - 2:14

score 285 · Answer 11 · 2021-05-06 18:19:47

285

Views

Infinite product expansion of $\frac{1}{\ln(x)}$?

Published on 06 May 2021 - 18:19

score 368 · Answer 12 · 2026-04-01 10:16:46

368

Views

Box topology and connectedness property

Published on 01 Apr 2026 - 10:16

score 66 · Answer 13 · 2021-05-10 21:35:46

66

Views

divergence of the series $\sum_{n=1}^{\infty}\dfrac{1}{\ln^{k}(n+1)}$ for any natural number $k$

Published on 10 May 2021 - 21:35

score 226 · Answer 14 · 2021-05-12 16:01:08

226

Views

Showing that an infinite product is holomorphic

Published on 12 May 2021 - 16:01

score 44 · Answer 15 · 2026-03-29 22:44:18

44

Views

Formula for $\prod_{n=0}^{\infty} (1 \pm x^n)$

Published on 29 Mar 2026 - 22:44

List Question

Finding the closed form of $\prod _{n=0}^{\infty }\left(1\:-\:x^{2^n}+x^{2^{n+1}}\right)$

Convergent Infinite Product in Proof of Partitions Identity

Proving that odd partitions and distinct partitions are equal

Closed form of the sum $\sum _{n=1}^{\infty }\:\left(\frac{1}{x^2-n^2\pi ^2}\right)$

Approximate result for $\prod_{n=1}^\infty\left(1-\frac{1}{2^n}\right)$?

Convergence of series $\sum \arcsin\left(\frac{r_n \sin(\theta_n)}{\sqrt{1+2r_n\cos(\theta_n)+r_n^2}}\right)$

e to an integral as an infinite product via the definition of the integral

Showing $\sinh z=z\prod_{n=1}^\infty\left(1+\frac{z^2}{n^2\pi^2}\right)$, given $\sin z=z\prod_{n=1}^{ \infty}\left(1 - \frac{z^2}{n^2\pi^2}\right)$

Translation symmetry by Gaussian integers for this infinite product is impossible by Liouville. What takes its place?

Solutions of $((a-1)!)^x=0$

Infinite product expansion of $\frac{1}{\ln(x)}$?

Box topology and connectedness property

divergence of the series $\sum_{n=1}^{\infty}\dfrac{1}{\ln^{k}(n+1)}$ for any natural number $k$

Showing that an infinite product is holomorphic

Formula for $\prod_{n=0}^{\infty} (1 \pm x^n)$

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