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Redundant Aunt
  • Member for 8 years, 9 months
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44 votes
3 answers
2k views

Show that $e^{\sqrt 2}$ is irrational

24 votes
1 answer
1k views

Proof of $\zeta(2)=\frac{\pi^2}{6}$

16 votes
2 answers
403 views

How to compute the following integral in $n$ variables?

15 votes
2 answers
315 views

How to prove $\int_{0}^{-1} \frac{\operatorname{Li}_2(x)}{(1-x)^2} dx=\frac{\pi^2}{24}-\frac{\ln^2(2)}{2} $

15 votes
4 answers
801 views

Does it make sense to define $ \aleph_{\infty}=\lim\limits_{n\to\infty}\aleph_n $? Is its cardinality "infinitely infinite"?

14 votes
2 answers
1k views

How to compute the monstrous $ \int_0^{\frac{e-1}{e}}{\frac{x(2-x)}{(1-x)}\frac{\log\left(\log\left(1+\frac{x^2}{2-2x}\right)\right)}{2-2x+x^2}dx} $

13 votes
2 answers
1k views

Ways to prove Euler's formula for $\zeta(2n)$

12 votes
3 answers
1k views

Function which takes every value uncountably often

11 votes
1 answer
167 views

Conjecture about natural number satisfying $ m(n)^k+1\space\mid\space n^{2k}+1 $

11 votes
4 answers
411 views

How to solve the functional equation $ f(f(x))=ax^2+bx+c $

11 votes
4 answers
433 views

Infinite sum involving number of solutions to $k=i^2+j^2$

10 votes
1 answer
439 views

How to prove that $\sum_{k=0}^\infty \binom{x}{x-k}\cdot\binom{x}{k-x} = 1$?

10 votes
3 answers
1k views

Harmonic number identity

10 votes
2 answers
215 views

How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$

9 votes
2 answers
105 views

On $\mathcal{A}$ with $\forall C\in\mathcal{P}_{\infty}(\mathbb{N})\exists A\in\mathcal{A}:A\cap C\in\mathcal{P}_{\infty}(\mathbb{N})$

8 votes
3 answers
1k views

Hard inequality $ (xy+yz+zx)\left(\frac{1}{(x+y)^2}+\frac{1}{(y+z)^2}+\frac{1}{(z+x)^2}\right)\ge\frac{9}{4} $

8 votes
3 answers
374 views

How to compute the integral $ I\left(c\right)=\int_{0}^{1}{\frac{\ln(1-cx)}{1+x}dx} $

8 votes
2 answers
905 views

What is the regularity of the greatest eigenvalue of the Hessian matrix?

8 votes
2 answers
157 views

Elegant proof of combinatorial statement: at least $l-k+1$ children who were in larger teams

7 votes
5 answers
4k views

How to show that $(W^\bot)^\bot=W$ (in a finite dimensional vector space)

7 votes
1 answer
173 views

Integral involving hyperfactorial

7 votes
3 answers
245 views

Calculate trigonometric integral $ \int_{-\infty}^{\infty}{\sin(x^2)}\,dx$

7 votes
1 answer
135 views

How to solve $\frac{f^{-1}(x)f(x)}{x}=\frac{f^{-1}(x)+f(x)}{2}$?

6 votes
2 answers
1k views

Variation of the Josephus problem

6 votes
1 answer
99 views

Differential equation related to Golomb's sequence

6 votes
0 answers
207 views

generalization of geometric series $ \sum_{k=0}^\infty x^{p(k)} $

6 votes
2 answers
247 views

Inequality $\frac{\sqrt a+\sqrt b+\sqrt c}{2}\ge\frac{1}{\sqrt a}+\frac{1}{\sqrt b}+\frac{1}{\sqrt c}$ with weird condition

6 votes
1 answer
287 views

How to evaluate the following infinite sum involving the Riemann zeta function?

6 votes
3 answers
470 views

How to prove $ \sum_{r=1}^{k-1} \binom{k}{r}\cdot r^r \cdot (k-r)^{k-r-1} = k^k-k^{k-1} $

6 votes
4 answers
137 views

Is g with $\cosh(xg(x))=x\cosh(g(x))$ decreasing?

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