Question

Analytic forms of $\frac{\sinh(2\pi/7)}{\sinh^{2}(3\pi/7)} - \frac{\sinh(\pi/7)}{\sinh^{2}(2\pi/7)} + \frac{\sinh(3\pi/7)}{\sinh^{2}(\pi/7)}$

score 178 · Answer 1 · 2013-07-27 02:45:37

178

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Analytic forms of $\frac{\sinh(2\pi/7)}{\sinh^{2}(3\pi/7)} - \frac{\sinh(\pi/7)}{\sinh^{2}(2\pi/7)} + \frac{\sinh(3\pi/7)}{\sinh^{2}(\pi/7)}$

Published on 27 Jul 2013 - 2:45

score 4.8k · Answer 2 · 2013-07-31 03:26:54

4.8k

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Are $\pi$ and $e$ algebraically independent?

Published on 31 Jul 2013 - 3:26

score 1.4k · Answer 3 · 2026-03-27 01:50:40

1.4k

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Prove that ${\sqrt2}^{\sqrt2}$ is an irrational number without using a theorem.

Published on 27 Mar 2026 - 1:50

score 205 · Answer 4 · 2013-08-03 22:28:30

205

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For integer $k > 1$, is $\sum_{i=0}^{\infty} 1/k^{2^i}$ transcendental or algebraic, or unknown?

Published on 03 Aug 2013 - 22:28

score 834 · Answer 5 · 2013-08-05 17:24:25

834

Views

Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?

Published on 05 Aug 2013 - 17:24

score 2.2k · Answer 6 · 2013-08-07 01:50:23

2.2k

Views

Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?

Published on 07 Aug 2013 - 1:50

score 213 · Answer 7 · 2013-08-07 18:52:50

213

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Please help me understand this proof that $e$ is transcendental

Published on 07 Aug 2013 - 18:52

score 1.4k · Answer 8 · 2013-08-08 01:21:20

1.4k

Views

Is there a proof that says that an operation that can take a transcendental number and make it an integer cannot exist?

Published on 08 Aug 2013 - 1:21

score 573 · Answer 9 · 2013-08-14 06:18:41

573

Views

The origin of $\pi$

Published on 14 Aug 2013 - 6:18

score 4.5k · Answer 10 · 2026-02-23 10:21:51

4.5k

Views

What if $\pi$ was an algebraic number? (significance of algebraic numbers)

Published on 23 Feb 2026 - 10:21

score 288 · Answer 11 · 2013-08-17 04:13:54

288

Views

Gelfond-Schneider Constant $2^{\sqrt{2}}$

Published on 17 Aug 2013 - 4:13

score 689 · Answer 12 · 2013-08-18 06:39:49

689

Views

Proof of $\pi$ not being a quadratic irrational number.

Published on 18 Aug 2013 - 6:39

score 314 · Answer 13 · 2013-08-19 22:15:35

314

Views

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Published on 19 Aug 2013 - 22:15

score 307 · Answer 14 · 2013-08-21 14:43:12

307

Views

Is $a^b$ transcendental when $a$ and $b$ are?

Published on 21 Aug 2013 - 14:43

score 115 · Answer 15 · 2026-03-26 04:53:07

115

Views

Are elements of the range of a transcendental function themselves transcendental, excepting a "few" special cases?

Published on 26 Mar 2026 - 4:53

List Question

Analytic forms of $\frac{\sinh(2\pi/7)}{\sinh^{2}(3\pi/7)} - \frac{\sinh(\pi/7)}{\sinh^{2}(2\pi/7)} + \frac{\sinh(3\pi/7)}{\sinh^{2}(\pi/7)}$

Are $\pi$ and $e$ algebraically independent?

Prove that ${\sqrt2}^{\sqrt2}$ is an irrational number without using a theorem.

For integer $k > 1$, is $\sum_{i=0}^{\infty} 1/k^{2^i}$ transcendental or algebraic, or unknown?

Is $\large \frac {\pi}{e}$ rational, irrational, or trandescendal?

Are the sums $\sum_{n=1}^{\infty} \frac{1}{(n!)^k}$ transcendental?

Please help me understand this proof that $e$ is transcendental

Is there a proof that says that an operation that can take a transcendental number and make it an integer cannot exist?

The origin of $\pi$

What if $\pi$ was an algebraic number? (significance of algebraic numbers)

Gelfond-Schneider Constant $2^{\sqrt{2}}$

Proof of $\pi$ not being a quadratic irrational number.

Is $\sum_{k=0}^{\infty}\frac1{2^{k^2}}$ rational? Transcendental?

Is $a^b$ transcendental when $a$ and $b$ are?

Are elements of the range of a transcendental function themselves transcendental, excepting a "few" special cases?

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