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Christian E. Ramirez's user avatar
Christian E. Ramirez's user avatar
Christian E. Ramirez's user avatar
Christian E. Ramirez
  • Member for 3 years, 8 months
  • Last seen this week
  • Ontario, Canada
24 votes

Evaluating $\int_0^1\int_0^1\cdots\int_0^1\frac{n\max\{x_1,x_2,\cdots,x_n\}}{x_1+x_2+\cdots+x_n}dx_1dx_2\cdots dx_n$

19 votes
Accepted

Is there an injective function $f:\mathbb{R}^2\rightarrow\mathbb{R}^2$ that maps circles to $n$-gons?

11 votes

An astounding identity: $\int_0^{\pi/2}\ln\lvert\sin(mx)\rvert\cdot \ln\lvert\sin(nx)\rvert\, dx$

9 votes
Accepted

Curiosities of the function $Q(x)=\sum_{n=1}^\infty \frac{P_n(x)}{n(2n+1)}$ where $P_n(x)$ is a sequence of all polynomials with unit coefficients

8 votes
Accepted

If $G$ is a finite group, show that there is some $g\in G$ so that $|G|\cdot |Sg \cap S| \leq |Sg|\cdot |S|$

8 votes
Accepted

A proof for the convergence of Eisenstein series

8 votes
Accepted

Degree of the minimal polynomial of $\sum\sqrt{2\pm\sqrt{2\pm\sqrt{2}}}$.

8 votes
Accepted

Is it possible that an infinite group has exactly one infinite nontrivial proper subgroup that has a certain order?

8 votes
Accepted

Show that all the nonzero roots of $f(x)$ are roots of unity. (A theorem of Kronecker)

7 votes
Accepted

Closed form of a power series involving double factorial: $\sum_{n=0}^{\infty} \frac{x^n}{(2n-1)!!}$

7 votes
Accepted

Write the sum $\sum\limits_{a \in \mathbb{N}}\sum\limits_{b \in \mathbb{N}} \frac{(a,b)}{a^sb^t}$ in terms of the Riemann zeta function

7 votes
Accepted

How to compute $\int_0^\pi \ln^2(\sin x)dx$ using complex analysis?

7 votes
Accepted

An interesting sum identity: $\sum \frac 1 {k_1\cdots k_m} = \sum_{k=1}^n \frac{(-1)^{k-1}}{k^m} \binom n k$

7 votes
Accepted

On an infinite harmonic series.

7 votes
Accepted

The intersection of all conjugates of a subgroup is of index at most $n!$

6 votes

Series involving derivative of Riemann Zeta function: $\displaystyle \sum_{k=2}^{\infty}\zeta'(k)x^{k-1}$

5 votes

Seeking more alternate proofs of a combinatorial generating function identity $G(x)=\overline{G}(-x)^{-1}$ related to counting strings.

5 votes
Accepted

How many different "syntactic trees" exist related to an $m$ word sentence?

5 votes
Accepted

Question about proving $\phi(mn) = \phi(m)\phi(n)$

5 votes
Accepted

Integral of $\exp(A t)$ with $A$ antisymetric $3\times 3$ matrix

4 votes
Accepted

Number of tuples that have odd sum

4 votes
Accepted

Is this general nested radical for $\pi$ true?

4 votes

How to evaluate $\int_{-\infty}^{+\infty}\frac{\cos x}{\left(1+x+x^2\right)^2+1}\mathrm{~d}x$

3 votes

Proving $\int_0^{\pi/2}\sin(nx)\arctan(\sin x)\,\mathrm{d}x=\dfrac{\pi(\sqrt{2}-1)^n}{2n}$ for odd $n$

3 votes

Guaranteed graph labyrinth solving sequence

3 votes

Simplifying $3S_1 + 2S_2 + 2S_3$, where $S_1=2\sum_{k=0}^n16^k\tan^4{2^kx}$, $S_2=4\sum_{k=0}^n16^k\tan^2{2^kx}$, $S_3=\sum_{k=0}^n16^k$

3 votes

Integral: $\int_{0}^{2\pi}\arctan\left(\frac{1+2\cos x}{\sqrt{3}}\right)dx$

3 votes
Accepted

Does implicit multiplication take precedence over functions?

2 votes
Accepted

Find sequence from the generating function $ A(x)= \dfrac{2x^2-x-2}{3x^3+2x^2+x-1}$

2 votes
Accepted

Continuity of parametric integral $I(\alpha)=\int_0^\infty \frac{\ln{(1-\alpha^2+\alpha^2x^2)}}{x^2-1}dx$