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Jack Rousseau
  • Member for 11 years, 2 months
  • Last seen more than 2 years ago
43 votes
7 answers
9k views

Evaluating the integral, $\int_{0}^{\infty} \ln\left(1 - e^{-x}\right) \,\mathrm dx $

9 votes
2 answers
3k views

Prove that $ \frac{n}{\phi(n)} = \sum\limits_{d \mid n} \frac{\mu^2(d)}{\phi(d)} $

8 votes
1 answer
3k views

Why is the determinant invariant under row and column operations?

5 votes
1 answer
1k views

Prove that a pentagon with congruent angles and rational sides is regular.

3 votes
2 answers
74 views

Proving the binomial coefficient identity $\binom{~s + t~ }{s} = \prod_{i=1}^s \prod_{j=1}^t \frac{i + j}{i + j - 1}$

3 votes
0 answers
553 views

Show that $n \sum\limits_{p \leq n} \frac{\log(p)}{p} = n \log(n) + \mathcal{O}(n)$

2 votes
3 answers
118 views

Show that $\mu(|f| \geq n)\rightarrow 0$ for $f \in L^p$.

2 votes
2 answers
3k views

Application of Holder's inequality.

2 votes
1 answer
53 views

Find explicit constants $A$ and $B$ such that any solution of $x^3 + 2y^3 = m$ satisfies $\max\{|x|,|y|\} \leq A|m|^B$.

2 votes
2 answers
96 views

Show that $f_n$ doesn't converge to $0$ in $L^p$ where $f_n = n^{-1/p}\chi_{[0,1]}$

2 votes
0 answers
234 views

A lower bound for continued fraction approximation.

1 vote
1 answer
2k views

Abelian group generated by $x,y,z$ with relations $-5x+6y+12z = 3x+4y+2z=11x+2y-8z=0$

1 vote
2 answers
1k views

Need help with proof showing that Lebesgue = Riemann integral.

0 votes
1 answer
464 views

Invertible bounded linear operators and closure

0 votes
1 answer
104 views

Show that a space $A$ is an integral domain.

0 votes
3 answers
140 views

Conjugation of polynomial in $\mathbb{Z}[x]$.