Question

Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$

score 1.7k · Answer 1 · 2026-04-01 12:38:00

1.7k

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Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$

Published on 01 Apr 2026 - 12:38

score 32 · Answer 2 · 2016-11-25 16:45:59

32

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Show that a function $F$ is continuous using a bound

Published on 25 Nov 2016 - 16:45

score 512 · Answer 3 · 2016-11-25 18:41:10

512

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A very short proof of $e$ is irrational

Published on 25 Nov 2016 - 18:41

score 29.4k · Answer 4 · 2016-11-26 05:08:12

29.4k

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Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.

Published on 26 Nov 2016 - 5:08

score 777 · Answer 5 · 2016-11-26 11:28:14

777

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Please verify my proof of: There is no integer $\geq2$ sum of squares of whose digits equal the integer itself.

Published on 26 Nov 2016 - 11:28

score 647 · Answer 6 · 2026-03-28 07:38:37

647

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How to prove $\sum\limits_{n=1}^\infty\frac{\sin(n)}n=\frac{\pi-1}2$ using only real numbers.

Published on 28 Mar 2026 - 7:38

score 295 · Answer 7 · 2026-03-27 19:33:32

295

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Alternative proof for $\Bbb R\ni x\mapsto e^{ix}\in S^1$ Lipschitz condition with $K=1$?

Published on 27 Mar 2026 - 19:33

score 342 · Answer 8 · 2016-11-27 23:45:47

342

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How do you prove this very different method for evaluating $\sum_{k=1}^nk^p$

Published on 27 Nov 2016 - 23:45

score 129 · Answer 9 · 2016-11-28 15:24:29

129

Views

An abstract algebraic proof that if for some positive integer $n$, $2^n - 1$ is prime, then so is $n$.

Published on 28 Nov 2016 - 15:24

score 83 · Answer 10 · 2016-11-28 18:01:29

83

Views

Proving one to one property of a function

Published on 28 Nov 2016 - 18:01

score 7.5k · Answer 11 · 2026-03-28 22:27:09

7.5k

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Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula

Published on 28 Mar 2026 - 22:27

score 325 · Answer 12 · 2016-12-01 17:13:56

325

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Convergence of $x_{n+2} = \sqrt{x_{n+1}} + \sqrt{x_{n}}$

Published on 01 Dec 2016 - 17:13

score 388 · Answer 13 · 2016-12-02 01:24:00

388

Views

Uniform Boundedness Principle for $L^p$

Published on 02 Dec 2016 - 1:24

score 69 · Answer 14 · 2016-12-02 13:07:24

69

Views

Shorter proof for expression of a circle in the complex plane

Published on 02 Dec 2016 - 13:07

score 272 · Answer 15 · 2016-12-03 00:30:10

272

Views

Necessary and sufficient condition for a set in $\mathbb{R}$ to be C-embedded or $C^*$-embedded

Published on 03 Dec 2016 - 0:30

List Question

Proof $\int_{-\infty}^\infty\frac{dx}{\left(e^x+e^{-x}+e^{ix\sqrt{3}}\right)^2}=\frac{1}{3}$

Show that a function $F$ is continuous using a bound

A very short proof of $e$ is irrational

Prove that $a^n-b^n = (a-b)(a^{n-1} + a^{n-2}b + \cdots + b^{n-1})$.

Please verify my proof of: There is no integer $\geq2$ sum of squares of whose digits equal the integer itself.

How to prove $\sum\limits_{n=1}^\infty\frac{\sin(n)}n=\frac{\pi-1}2$ using only real numbers.

Alternative proof for $\Bbb R\ni x\mapsto e^{ix}\in S^1$ Lipschitz condition with $K=1$?

How do you prove this very different method for evaluating $\sum_{k=1}^nk^p$

An abstract algebraic proof that if for some positive integer $n$, $2^n - 1$ is prime, then so is $n$.

Proving one to one property of a function

Methods to compute $\sum_{k=1}^nk^p$ without Faulhaber's formula

Convergence of $x_{n+2} = \sqrt{x_{n+1}} + \sqrt{x_{n}}$

Uniform Boundedness Principle for $L^p$

Shorter proof for expression of a circle in the complex plane

Necessary and sufficient condition for a set in $\mathbb{R}$ to be C-embedded or $C^*$-embedded

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