User Winther

51 votes

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Proof (claimed) for Riemann hypothesis on ArXiv

answered Aug 22, 2016 at 14:23

38 votes

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Integration and differentiation of Fourier series

answered May 3, 2016 at 22:54

31 votes

The expected outcome of a random game of chess?

answered Jun 25, 2014 at 6:31

25 votes

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An integral identity from Ramanujan's notebooks

answered Sep 2, 2015 at 13:02

19 votes

$f(f(f(x))) = x$. Prove or disprove that f is the identity function

answered Apr 30, 2017 at 5:03

15 votes

An integral identity from Ramanujan's notebooks

answered Sep 2, 2015 at 18:05

15 votes

The limit of $(n!)^{1/n}/n$ as $n\to\infty$

answered Sep 17, 2014 at 20:44

15 votes

Accepted

Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$

answered Jan 13, 2015 at 10:58

14 votes

If $\sum_{n_0}^{\infty} a_n$ diverges prove that $\sum_{n_0}^{\infty} \frac{a_n}{a_1+a_2+...+a_n} = +\infty $

answered Jan 10, 2016 at 12:58

14 votes

Accepted

A Neat Identity Involving Zeta Zeroes

answered Sep 15, 2016 at 17:07

14 votes

Intuition behind the paradox of instantaneous heat propagation

answered Oct 19, 2019 at 21:46

14 votes

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How can I prove that $\int_{0}^{\infty }\frac{\log(1+x)}{x(1+x)}dx=\sum_{n=1}^{\infty }\frac{1}{n^2}$

answered Jan 5, 2015 at 22:14

14 votes

Accepted

Prove $\alpha \in\mathbb R$ is irrational, when $\cos(\alpha \pi) = \frac{1}{3}$

answered Sep 1, 2014 at 22:03

12 votes

Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$

answered Mar 11, 2015 at 3:13

12 votes

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Principal branch of logarithm

answered Oct 11, 2015 at 23:49

12 votes

Accepted

How to prove this inequality $x^2_{n}\le\frac{8}{3}$

answered Apr 8, 2020 at 19:57

12 votes

Accepted

Equality of laplace transform

answered Jan 4, 2015 at 0:08

11 votes

Let $f$ be a function such that $f'(x)=\frac{1}{x}$ and $f(1) = 0$ , show that $f(xy) = f(x) + f(y)$

answered Jun 12, 2015 at 23:41

11 votes

Accepted

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

answered Jan 4, 2016 at 7:32

11 votes

Could a square be a perfect number?

answered Mar 17, 2016 at 17:57

11 votes

Evaluating $\int_{-\infty}^\infty\frac1{1+x^2+x^4+\cdots}\ \text{dx}$

answered Dec 23, 2016 at 13:10

10 votes

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Find $a_{n,i,j}$ in the expansion $(x + D)^n = \sum\limits_{i,j} a_{n,i,j} x^i D^j.$

answered Jul 15, 2015 at 23:43

10 votes

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Proving that $\sum_{n=0}^{\infty }\frac{3(n!)^2}{(2n+2)!}=\sum_{n=1}^{\infty }\frac{1}{n^2}=\frac{\pi ^2}{6}$

answered Sep 28, 2015 at 23:17

10 votes

Accepted

Prove that $f(x)=\sum_\limits{n=1}^{\infty} \frac{1}{x^2+n^2}$ is differentiable on $\mathbb{R}$

answered Feb 28, 2016 at 16:01

10 votes

Accepted

Find $\lfloor 1000S \rfloor$ for $S =\sum_{n=1}^{\infty} \frac{1}{2^{n^2}} = \frac{1}{2^1}+\frac{1}{2^4}+\frac{1}{2^9}+\cdots.$

answered Jan 10, 2016 at 0:32

10 votes

Accepted

Prove that: $\zeta(3)=\lim_{N\to \infty}{1\over N}\sum_{k=1}^{N}{1\over k^{\phi^2}\ln{\left(1+{k^{\phi^{-2}}\over N}\right)}}$

answered Dec 27, 2016 at 21:51

10 votes

Accepted

Why do $x^{x^{x^{\dots}}}=2$ and $x^{x^{x^{\dots}}}=4$ have the same positive root $\sqrt 2$?

answered Jul 10, 2016 at 18:19

10 votes

Accepted

Prove that $\exp(A+B)=\exp(A)\exp(B)$ iff $[A,B] = 0$

answered Jun 23, 2016 at 2:41

10 votes

Accepted

Bound on matrix product $\begin{bmatrix} 1+\frac{1}{n} & -1 \\ 1 & 0 \end{bmatrix}\cdots\begin{bmatrix} 1+\frac{1}{2} & -1 \\ 1 & 0 \end{bmatrix}$

answered Apr 8, 2020 at 4:11

9 votes

Accepted

Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$

answered Dec 9, 2015 at 2:23

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563 Answers

Proof (claimed) for Riemann hypothesis on ArXiv

Integration and differentiation of Fourier series

The expected outcome of a random game of chess?

An integral identity from Ramanujan's notebooks

$f(f(f(x))) = x$. Prove or disprove that f is the identity function

An integral identity from Ramanujan's notebooks

The limit of $(n!)^{1/n}/n$ as $n\to\infty$

Proving that $\int_0^1 f(x)e^{nx}\,{\rm d}x = 0$ for all $n\in\mathbb{N}_0$ implies $f(x) = 0$

If $\sum_{n_0}^{\infty} a_n$ diverges prove that $\sum_{n_0}^{\infty} \frac{a_n}{a_1+a_2+...+a_n} = +\infty $

A Neat Identity Involving Zeta Zeroes

Intuition behind the paradox of instantaneous heat propagation

How can I prove that $\int_{0}^{\infty }\frac{\log(1+x)}{x(1+x)}dx=\sum_{n=1}^{\infty }\frac{1}{n^2}$

Prove $\alpha \in\mathbb R$ is irrational, when $\cos(\alpha \pi) = \frac{1}{3}$

Prove that $|a+b|^p \leq 2^p \{ |a|^p +|b|^p \}$

Principal branch of logarithm

How to prove this inequality $x^2_{n}\le\frac{8}{3}$

Equality of laplace transform

Let $f$ be a function such that $f'(x)=\frac{1}{x}$ and $f(1) = 0$ , show that $f(xy) = f(x) + f(y)$

Closed form for $\sum^\infty_{n=1}\frac{H_n}{2^n\,(2n+1)^2}$

Could a square be a perfect number?

Evaluating $\int_{-\infty}^\infty\frac1{1+x^2+x^4+\cdots}\ \text{dx}$

Find $a_{n,i,j}$ in the expansion $(x + D)^n = \sum\limits_{i,j} a_{n,i,j} x^i D^j.$

Proving that $\sum_{n=0}^{\infty }\frac{3(n!)^2}{(2n+2)!}=\sum_{n=1}^{\infty }\frac{1}{n^2}=\frac{\pi ^2}{6}$

Prove that $f(x)=\sum_\limits{n=1}^{\infty} \frac{1}{x^2+n^2}$ is differentiable on $\mathbb{R}$

Find $\lfloor 1000S \rfloor$ for $S =\sum_{n=1}^{\infty} \frac{1}{2^{n^2}} = \frac{1}{2^1}+\frac{1}{2^4}+\frac{1}{2^9}+\cdots.$

Prove that: $\zeta(3)=\lim_{N\to \infty}{1\over N}\sum_{k=1}^{N}{1\over k^{\phi^2}\ln{\left(1+{k^{\phi^{-2}}\over N}\right)}}$

Why do $x^{x^{x^{\dots}}}=2$ and $x^{x^{x^{\dots}}}=4$ have the same positive root $\sqrt 2$?

Prove that $\exp(A+B)=\exp(A)\exp(B)$ iff $[A,B] = 0$

Bound on matrix product $\begin{bmatrix} 1+\frac{1}{n} & -1 \\ 1 & 0 \end{bmatrix}\cdots\begin{bmatrix} 1+\frac{1}{2} & -1 \\ 1 & 0 \end{bmatrix}$

Roots of unity filter, identity involving $\sum_{k \ge 0} \binom{n}{3k}$