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Winther's user avatar
Winther's user avatar
Winther
  • Member for 10 years, 2 months
  • Last seen this week
51 votes
Accepted

Proof (claimed) for Riemann hypothesis on ArXiv

39 votes
Accepted

Integration and differentiation of Fourier series

31 votes

The expected outcome of a random game of chess?

25 votes
Accepted

An integral identity from Ramanujan's notebooks

21 votes

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

16 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 $

16 votes

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

15 votes
Accepted

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

15 votes

An integral identity from Ramanujan's notebooks

15 votes

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

14 votes
Accepted

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

14 votes
Accepted

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

14 votes
Accepted

A Neat Identity Involving Zeta Zeroes

14 votes

Intuition behind the paradox of instantaneous heat propagation

13 votes
Accepted

Equality of laplace transform

13 votes

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

13 votes
Accepted

Principal branch of logarithm

12 votes

How to find continued fraction of pi

12 votes
Accepted

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

11 votes
Accepted

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

11 votes

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

11 votes

Could a square be a perfect number?

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

10 votes
Accepted

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

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