User Frpzzd

298

votes

23

answers

11k

views

Why don't we define “imaginary” numbers for every “impossibility”?

soft-question

Feb 5 '18 at 13:06 Peter Smith 40.8k

281

votes

101

answers

25k

views

Surprising identities / equations

soft-question big-list

1d ago coffeee 103

211

votes

15

answers

25k

views

Really advanced techniques of integration (definite or indefinite)

integration soft-question definite-integrals indefinite-integrals big-list

Oct 16 at 4:08 clathratus 4,583

171

votes

6

answers

8k

views

How could we define the factorial of a matrix?

linear-algebra matrices operator-theory factorial matrix-calculus

Sep 23 at 14:54 Travis 60.5k

147

votes

4

answers

13k

views

Some users are mind bogglingly skilled at integration. How did they get there?

integration soft-question definite-integrals

Dec 21 '16 at 20:22 Community♦ 1

131

votes

3

answers

27k

views

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

analysis integration definite-integrals closed-form zeta-functions

Aug 29 '14 at 22:31 Community♦ 1

110

votes

1

answer

3k

views

Is There An Injective Cubic Polynomial $\mathbb Z^2 \rightarrow \mathbb Z$?

number-theory polynomials

Nov 29 '15 at 5:18 Milo Brandt 39.8k

92

votes

5

answers

22k

views

The sum of an uncountable number of positive numbers

measure-theory summation

Feb 12 at 9:22 Javi 2,699

83

votes

3

answers

2k

views

How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$

sequences-and-series limits recurrence-relations

Oct 11 '16 at 15:39 Michael Rozenberg 104k

76

votes

2

answers

24k

views

Predicting Real Numbers

sequences-and-series recreational-mathematics puzzle axiom-of-choice

Jul 31 at 17:01 StevenClontz 564

68

votes

18

answers

23k

views

Why do we need to learn integration techniques?

calculus integration soft-question education

Nov 27 at 14:20 Robert Wolfe 5,827

42

votes

2

answers

3k

views

Proving a jigsaw is possible

combinatorics recreational-mathematics puzzle

Dec 13 at 20:44 Jean Marie 29.9k

35

votes

3

answers

918

views

What's the limit of $\sqrt{2 + \sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2 + …}}}}}} $?

calculus real-analysis limits closed-form nested-radicals

Nov 23 '17 at 21:03 Γιώργος Πλούσος 11

32

votes

5

answers

928

views

A disease spreading through a triangular population

probability combinatorics graph-theory asymptotics expectation

May 12 '16 at 13:26 Community♦ 1

29

votes

6

answers

5k

views

Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$

polynomials functional-equations contest-math

Oct 12 '15 at 16:54 Community♦ 1

26

votes

1

answer

688

views

Prove that $ \sum\limits_{n=-\infty}^\infty\frac{\cos\pi\sqrt{n^2+1}}{3+4n^2}=\int\limits_{-\infty}^\infty\frac{\cos\pi\sqrt{x^2+1}}{3+4x^2}dx $?

calculus real-analysis integration sequences-and-series

Nov 28 '17 at 14:55 achille hui 96k

25

votes

4

answers

770

views

Proof of $\int_0^\infty \frac{x^{\alpha}dx}{1+2x\cos\beta +x^{2}}=\frac{\pi\sin (\alpha\beta)}{\sin (\alpha\pi)\sin \beta }$

calculus real-analysis integration definite-integrals improper-integrals

Jan 25 '17 at 15:06 Community♦ 1

24

votes

2

answers

835

views

Prove that the expression is a perfect square

algebra-precalculus elementary-number-theory functions

Jan 6 '18 at 20:09 Colm Bhandal 3,371

23

votes

4

answers

1k

views

Suggestions for mathematical solitaire against boredom

soft-question recreational-mathematics

Aug 2 '17 at 22:10 richard1941 517

22

votes

3

answers

529

views

Ways to show that $\int_{0}^{1}((1-x^r)^{1/r}-x)^ndx=\frac{1}{n+1}$

calculus integration definite-integrals

Jan 28 at 0:56 Sangchul Lee 94.1k

22

votes

2

answers

450

views

Does recursively replacing $\frac1n$ by $\frac1n(\frac12+\dots+\frac1{n+1})$ really converge to $\frac1e$?

real-analysis sequences-and-series convergence

Aug 19 at 16:36 Markus Scheuer 61.9k

22

votes

3

answers

738

views

Calculate moment of inertia of Koch snowflake

physics recreational-mathematics fractals fractal-analysis

May 19 '16 at 2:35 Bennett Gardiner 3,064

20

votes

3

answers

291

views

Evaluate $\lim\limits_{x\to\infty}\frac1x\int_0^x\max\{\sin t,\sin(t\sqrt2)\}dt$

calculus integration definite-integrals

Jul 23 at 10:47 Sangchul Lee 94.1k

17

votes

3

answers

292

views

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

algebra-precalculus inequality recreational-mathematics absolute-value substitution

Oct 3 at 0:48 farruhota 20.4k

16

votes

5

answers

291

views

Bounds (and range) of a nonlinear difference equation

recurrence-relations dynamical-systems periodic-functions

Nov 18 '17 at 0:54 Somos 14k

16

votes

2

answers

533

views

prove this $\sum_{n=1}^{\infty}\arctan{\left(\dfrac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\dfrac{\sqrt{2}-1}{2}}\right)\cdots\right)}$

summation

Dec 20 '13 at 9:05 achille hui 96k

15

votes

1

answer

192

views

Evaluating $\int_0^{\pi/2} \int_0^{\pi/2} \frac{\cos(x)}{ \cos(a \cos(x) \cos(y))} dx dy $

calculus real-analysis integration definite-integrals

Oct 6 '14 at 23:45 Community♦ 1

15

votes

5

answers

326

views

Finding the minimal number of members

combinatorics

Dec 13 at 14:56 antkam 1,762

14

votes

1

answer

367

views

On solvable octic trinomials like $x^8-5x-5=0$

galois-theory radicals

Dec 20 at 6:29 klajok 370

14

votes

2

answers

311

views

Is $a_n=\sum_{\alpha=0}^n\;\text{round}(\sin\alpha)$ bounded?

sequences-and-series

Feb 5 at 3:56 dmtri 1,508

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Why don't we define “imaginary” numbers for every “impossibility”?

Surprising identities / equations

Really advanced techniques of integration (definite or indefinite)

How could we define the factorial of a matrix?

Some users are mind bogglingly skilled at integration. How did they get there?

Evaluate $\int_0^1 \frac{\log \left( 1+x^{2+\sqrt{3}}\right)}{1+x}\mathrm dx$

Is There An Injective Cubic Polynomial $\mathbb Z^2 \rightarrow \mathbb Z$?

The sum of an uncountable number of positive numbers

How prove this nice limit $\lim\limits_{n\to\infty}\frac{a_{n}}{n}=\frac{12}{\log{432}}$

Predicting Real Numbers

Why do we need to learn integration techniques?

Proving a jigsaw is possible

What's the limit of $\sqrt{2 + \sqrt{2-\sqrt{2+\sqrt{2-\sqrt{2-\sqrt{2 + …}}}}}} $?

A disease spreading through a triangular population

Find all polynomials $P$ such that $P(x^2+1)=P(x)^2+1$

Prove that $ \sum\limits_{n=-\infty}^\infty\frac{\cos\pi\sqrt{n^2+1}}{3+4n^2}=\int\limits_{-\infty}^\infty\frac{\cos\pi\sqrt{x^2+1}}{3+4x^2}dx $?

Proof of $\int_0^\infty \frac{x^{\alpha}dx}{1+2x\cos\beta +x^{2}}=\frac{\pi\sin (\alpha\beta)}{\sin (\alpha\pi)\sin \beta }$

Prove that the expression is a perfect square

Suggestions for mathematical solitaire against boredom

Ways to show that $\int_{0}^{1}((1-x^r)^{1/r}-x)^ndx=\frac{1}{n+1}$

Does recursively replacing $\frac1n$ by $\frac1n(\frac12+\dots+\frac1{n+1})$ really converge to $\frac1e$?

Calculate moment of inertia of Koch snowflake

Evaluate $\lim\limits_{x\to\infty}\frac1x\int_0^x\max\{\sin t,\sin(t\sqrt2)\}dt$

Quadratic inequality puzzle: Prove$ |cx^2 + bx + a| ≤ 2$ given $|ax^2+bx+c| ≤ 1$

Bounds (and range) of a nonlinear difference equation

prove this $\sum_{n=1}^{\infty}\arctan{\left(\dfrac{1}{n^2+1}\right)}=\arctan{\left(\tan\left(\pi\sqrt{\dfrac{\sqrt{2}-1}{2}}\right)\cdots\right)}$

Evaluating $\int_0^{\pi/2} \int_0^{\pi/2} \frac{\cos(x)}{ \cos(a \cos(x) \cos(y))} dx dy $

Finding the minimal number of members

On solvable octic trinomials like $x^8-5x-5=0$

Is $a_n=\sum_{\alpha=0}^n\;\text{round}(\sin\alpha)$ bounded?