User Ian Mateus

33

149

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7

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14k

views

Does a “cubic” matrix exist?

tensors multilinear-algebra

Jun 11 '17 at 16:53 Sasha 66.6k

18

54

votes

12

answers

5k

views

Is there any geometric way to characterize $e$?

real-analysis algebra-precalculus

May 8 at 13:07 Penelope Benenati 183

3

21

votes

2

answers

445

views

Mystery about $\sum_{n\geqslant 1}2^{-n!}$

sequences-and-series number-theory

Nov 24 '13 at 2:44 TMM 9,624

2

20

votes

3

answers

872

views

Rigorous proof that $\frac{1}{3} = 0.333\ldots$

algebra-precalculus sequences-and-series

Mar 12 '18 at 18:25 fleablood 114k

7

17

votes

1

answer

353

views

$\sqrt[2]{1+\sqrt[3]{1+\sqrt[4]{1+\cdots}}}\approx 1.5176001678…$

sequences-and-series limits

Jul 31 '13 at 7:55 Daniel Robert-Nicoud 27.1k

7

16

votes

4

answers

472

views

Evaluating $\sum_{k=1}^{\infty}\frac{\sin\left(k\theta\right)}{k^{2u+1}}$ with multiple integrals

sequences-and-series zeta-functions

Apr 11 '14 at 19:54 Community♦ 1

4

11

votes

3

answers

609

views

A probabilistic integral $\int_{-\infty}^{\infty}e^{-x^2/2\sigma^2}\arcsin\left(1-2\left|\lfloor x\rceil-x\right|\right)\,dx$

integration definite-integrals improper-integrals

Aug 12 '14 at 2:30 Community♦ 1

1

9

votes

2

answers

3k

views

Sum of squares of roots of a polynomial $P(x)$

algebra-precalculus polynomials

Jul 29 at 4:17 Nedi Sawego Yogya 11

3

9

votes

5

answers

697

views

Proving that $a + b = b + a$ for all $a,b \in\mathbb{R}$

real-analysis definition

Jun 16 '12 at 19:06 Community♦ 1

1

8

votes

3

answers

4k

views

Sum of irrational numbers

algebra-precalculus irrational-numbers alternative-proof

Jan 17 '15 at 0:35 Community♦ 1

3

8

votes

2

answers

307

views

Do we know a number $n\gt 5$ with no twin prime $n\lt q\lt 2n$?

number-theory prime-numbers

Feb 4 '14 at 22:19 Community♦ 1

8

votes

4

answers

468

views

Is it correct to say that $\mathbb{R}$ has fewer elements than $\mathbb{C}$ if both are infinite?

elementary-set-theory complex-numbers

Oct 17 '11 at 0:53 J. M. isn't a mathematician 69.6k

7

votes

3

answers

380

views

Putting ${n \choose 0} + {n \choose 5} + {n \choose 10} + \cdots + {n \choose 5k} + \cdots$ in a closed form

complex-numbers binomial-coefficients

May 21 '17 at 10:39 Did 265k

2

7

votes

2

answers

751

views

How can we directly see that the number of random walks starting and ending at the origin is ${n\choose n/2}^2$?

combinatorics random-walk

Oct 6 '13 at 0:15 Jean-Sébastien 4,403

2

5

votes

3

answers

2k

views

Do “complex percentages” exist?

complex-numbers

Feb 8 '16 at 23:09 ngb 1

1

5

votes

2

answers

171

views

How many values does $1^{\alpha}$ have for $\alpha$ irrational?

complex-analysis exponentiation branch-cuts

Dec 29 '13 at 18:41 Ian Mateus 6,905

1

5

votes

4

answers

312

views

Why can't partial fractions expansion be “normally” done is this case?

algebra-precalculus partial-fractions

Feb 14 '12 at 19:57 Aryabhata 77.2k

2

4

votes

2

answers

233

views

Evaluating $\sum_{j\geqslant1}\sum_{k\geqslant1}(-1)^{k+j}\frac{(2k-1)+i(2j-1)}{((2k-1)^{2}+(2j-1)^{2})^{3/2}}.$

complex-numbers summation

Aug 28 '14 at 20:54 Community♦ 1

4

votes

1

answer

149

views

How can I write $e^{ki\theta}/k$ as a nice integral?

limits improper-integrals

Jan 10 '13 at 17:23 Ilya 32.7k

2

4

votes

1

answer

261

views

Prove for $x$, $y$ and $z$

algebra-precalculus

Feb 18 '12 at 8:18 Community♦ 1

2

votes

1

answer

481

views

What does the convergence of a Dirichlet series tells us about the convergence of a power series?

complex-analysis convergence-divergence power-series

Jul 13 '17 at 11:53 Daniel Fischer♦ 194k

1

2

votes

3

answers

254

views

Solving the system $(18xy^2+x^3, 27x^2y+54y^3)=(12, 38)$

systems-of-equations cubic-equations

Jan 27 '14 at 21:25 Community♦ 1

1

2

votes

2

answers

193

views

Choosing convenient limits of integration on Basel problem

sequences-and-series algebra-precalculus

Jan 13 '13 at 22:04 Community♦ 1

1

vote

2

answers

110

views

Is $\lim_{x\rightarrow\infty}\prod_{p\leqslant x}p^{1/x}$ finite?

number-theory limits

Sep 21 '13 at 22:56 leshik 4,710

1

vote

2

answers

179

views

Combinatorics thinking

combinatorics

Jul 2 '12 at 16:02 Christian Blatter 211k

0

votes

1

answer

60

views

Is it possible to define side-euclidean divisions in square matrices?

abstract-algebra matrices

Feb 5 '14 at 21:20 Ian Mateus 6,905

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26 Questions

Does a “cubic” matrix exist?

Is there any geometric way to characterize $e$?

Mystery about $\sum_{n\geqslant 1}2^{-n!}$

Rigorous proof that $\frac{1}{3} = 0.333\ldots$

$\sqrt[2]{1+\sqrt[3]{1+\sqrt[4]{1+\cdots}}}\approx 1.5176001678…$

Evaluating $\sum_{k=1}^{\infty}\frac{\sin\left(k\theta\right)}{k^{2u+1}}$ with multiple integrals

A probabilistic integral $\int_{-\infty}^{\infty}e^{-x^2/2\sigma^2}\arcsin\left(1-2\left|\lfloor x\rceil-x\right|\right)\,dx$

Sum of squares of roots of a polynomial $P(x)$

Proving that $a + b = b + a$ for all $a,b \in\mathbb{R}$

Sum of irrational numbers

Do we know a number $n\gt 5$ with no twin prime $n\lt q\lt 2n$?

Is it correct to say that $\mathbb{R}$ has fewer elements than $\mathbb{C}$ if both are infinite?

Putting ${n \choose 0} + {n \choose 5} + {n \choose 10} + \cdots + {n \choose 5k} + \cdots$ in a closed form

How can we directly see that the number of random walks starting and ending at the origin is ${n\choose n/2}^2$?

Do “complex percentages” exist?

How many values does $1^{\alpha}$ have for $\alpha$ irrational?

Why can't partial fractions expansion be “normally” done is this case?

Evaluating $\sum_{j\geqslant1}\sum_{k\geqslant1}(-1)^{k+j}\frac{(2k-1)+i(2j-1)}{((2k-1)^{2}+(2j-1)^{2})^{3/2}}.$

How can I write $e^{ki\theta}/k$ as a nice integral?

Prove for $x$, $y$ and $z$

What does the convergence of a Dirichlet series tells us about the convergence of a power series?

Solving the system $(18xy^2+x^3, 27x^2y+54y^3)=(12, 38)$

Choosing convenient limits of integration on Basel problem

Is $\lim_{x\rightarrow\infty}\prod_{p\leqslant x}p^{1/x}$ finite?

Combinatorics thinking

Is it possible to define side-euclidean divisions in square matrices?